Hagen Fogler Froment Bird

fig_001.png

hffb_ue.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ueb. Hagen Fogler Froment Bird\n",
    "\n",
    "[1] Hagen, Jens: Chemiereaktoren : Auslegung und Simulation. New York: John Wiley & Sons, 2012.\n",
    "\n",
    "[2] Fogler, H. Scott: Essentials of Chemical Reaction Engineering. Amsterdam: Pearson Education, 2011.\n",
    "\n",
    "[3] Froment, Gilbert F. ; Bischoff, Kenneth B. ; Wilde, Juray De: Chemical Reactor Analysis and Design. New York: Wiley, 2010.\n",
    "\n",
    "[4] Bird, R. Byron ; Stewart, Warren E. ; Lightfoot, Edwin N.: Transport Phenomena. New York: John Wiley & Sons, 2007.\n",
    "\n",
    "[5] e.V., VDI: VDI-Wärmeatlas. Wiesbaden: Springer Berlin Heidelberg, 2013.\n",
    "\n",
    "[6] Baerns, Manfred ; Behr, Arno ; Brehm, Axel ; Gmehling, Jürgen ; Hinrichsen, Kai-Olaf ; Hofmann, Hanns ; Onken, Ulfert ; Palkovits, Regina ; Renken, Albert: Technische Chemie. New York: John Wiley & Sons, 2014."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ü 5.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Für die Reaktion $A \\rightarrow R$ ist k = 0,02 $min^{-1}$. Es sollen in 10 h 4752 mol R produziert werden, $U_A = 0,99$. Die Rüstzeit beträgt 1,16 h, $c_{A,0} = 8 mol/L$. Welches Reaktions-\n",
    "volumen wird für einen diskontinuierlich betriebenen Rührkessel benötigt?\n",
    "\n",
    "dnA/dt = (-1) r Vr\n",
    "\n",
    "dnR/dt = (+1) r Vr\n",
    "\n",
    "(nA0 - nA)/nA0 = UA = 1-nA/nA0\n",
    "\n",
    "nA = (1-UA)nA0\n",
    "\n",
    "\n",
    "-nA0 dUA/dt = (-1) r Vr\n",
    "\n",
    "\n",
    "dUA/dt = k (nA/Vr) Vr/nA0\n",
    "\n",
    "dUA/dt = k (1-UA)\n",
    "\n",
    "d(1-UA)/dt = -dUA/dt = -k (1-UA)\n",
    "\n",
    "1/(1-UA) d(1-UA) = -k dt\n",
    "\n",
    "ln(1-UA) + ln(1-0) = -k tau\n",
    "\n",
    "1-UA = exp(-k tau)\n",
    "\n",
    "UA = 1-exp(-k tau)\n",
    "\n",
    "\n",
    "tau = -ln(1-UA)/k\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$A \\rightarrow P$\n",
    "\n",
    "$V_R = (t_R - t_V)\\frac{\\dot{n_p} (-\\nu_a)}{U_A S_P C_{A0} \\nu_P}$\n",
    "\n",
    "$S_P = \\frac{\\dot{n_P} (-\\nu_A)}{(n_{A,0}-n_A)\\nu_P}$\n",
    "\n",
    "$U_A = \\frac{n_{A,0}-n_A}{n_{A,0}} = \\frac{n_{A,0}-n_{A,0}-\\nu_A\\xi_1}{n_{A,0}} $\n",
    "\n",
    "$A_P = \\frac{n_P/\\nu_P}{n_A/(-\\nu_A)} = U_A S_P$\n",
    "\n",
    "==>> $V_R = (t_R + t_V)\\frac{\\dot{n_P} (-\\nu_A)}{\\left(\\frac{n_P/\\nu_P}{n_A/(-\\nu_A)} \\right)} = (t_R + t_V)\\left( \\frac{\\dot{n_P}}{n_P} \\right) \\left( \\frac{\\dot{n_{A,0}}}{c_{A,0}} \\right)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tR = 3.83764h\n",
      "tV = 1.16h\n",
      "UA = 0.99\n",
      "Vr= 299.859L\n",
      "nbatches=2.00094\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "ua = 0.99\n",
    "tau = -np.log(1-ua)/0.02 # min\n",
    "tv = 1.16*60\n",
    "ndotp = 4752/(10*60.0)\n",
    "vr = (tau+tv)*ndotp/(8*0.99) # L\n",
    "nbatches = 10*60/(tau+tv)\n",
    "print ('tR = ' + '{0:g}'.format(tau / 60.0) + 'h')\n",
    "print ('tV = ' + '{0:g}'.format(1.16) + 'h')\n",
    "print ('UA = ' + '{0:g}'.format(ua))\n",
    "print ('Vr= ' + '{0:g}'.format(vr) + 'L')\n",
    "print ('nbatches=' + '{0:g}'.format(nbatches))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ü 5.3\n",
    "\n",
    "$A(g) \\rightarrow 3 B(g) \\hspace{2cm} -r_A = (0,6min^{-1}) C_A$\n",
    "\n",
    "$\\dot{V_0} C_{A,0} = 9mol/min$, $C_{A,0}=0,5mol/L$ , $U_A = 0,667$ \n",
    "\n",
    "==>> $\\dot{V_0} = \\dot{V_0} C_{A,0}/C_{A,0} = (9/0,5) L/min$\n",
    "\n",
    "**Mit Volumenveränderung**\n",
    "\n",
    "$Z=\\frac{P V}{n R T}$\n",
    "\n",
    "$\\frac{\\dot{V}}{\\dot{V_0}}=\\left(\\frac{\\dot{n}}{\\dot{n_0}}\\right)\\left(\\frac{T}{T_0}\\right)\\left(\\frac{P_0}{P}\\right)\\left(\\frac{Z}{Z_0}\\right)$\n",
    "\n",
    "$\\frac{\\dot n}{\\dot n_0}=\\frac{n_0 + (\\sum_i{\\nu_i})\\xi_1}{n_0} = 1 + \\frac{(\\sum_i{\\nu_i})\\xi_1}{n_0}$\n",
    "\n",
    "$U_A=\\frac{n_{A,0} - n_{A,0} - \\nu_A \\xi_1}{n_{A,0}} \\rightarrow \\xi_1=U_A\\frac{n_{A,0}}{(-\\nu_A)}$ \n",
    "\n",
    "$\\frac{\\dot n}{\\dot n_0}= 1 + \\frac{(\\sum_i{\\nu_i})}{(-\\nu_A)}\\frac{n_{A,0}}{n_0}U_A= 1 + \\frac{(\\sum_i{\\nu_i})}{(-\\nu_A)}x_{A,0}U_A$\n",
    "\n",
    "$\\epsilon_A \\equiv \\frac{(\\sum_i{\\nu_i})}{(-\\nu_A)}$\n",
    "\n",
    "Vorausgesetzt, dass das Zulaufstrom und Auslassstrom konstant bleiben (somit auch das Volumen des Reaktors). Im zeitunabhängigen Zustand sollen beide Ströme folgende Werte vertreten: Zulaufstrom $\\dot{V_0}(1+\\epsilon_A U_A)$, Auslassstrom $\\dot{V_0}(1+\\epsilon_A U_A)$. Wie ist es dazu gekommen, dass das Zulaufstrom wächst, ohne dass die Temperatur ansteigt?. Vielleicht sind variabler Druck oder variable Temperatur im Zulaufstrom für diesen Ansatz notwendig. Sonst müsste man ein unterschiedliches Volumen im Zulaufstrom eingeben, als man im Auslassstrom hinauszieht: $\\dot{V_0}=18L/min$, $\\dot{V_0}(1+\\epsilon_A U_A)=42.012L/min$.\n",
    "\n",
    "$\\frac{d n_A}{d t} = 0 = \\dot{n_{A,0}} - \\dot{n_A} +  \\nu_A \\times r \\times V_R$\n",
    "\n",
    "$0 = \\dot{V} C_{A,0} - \\dot{V} C_A   +  \\nu_A \\times r \\times V_R = \\dot{V_0} (1 + \\epsilon_A x_{A,0} U_A) U_A C_{A,0} +  \\nu_A \\times r \\times V_R$\n",
    "\n",
    "$V_R = \\frac{\\dot{V_0} U_A C_{A,0} (1 + \\epsilon_A U_A)}{(-\\nu_A)k C_A} = \\frac{\\dot{V_0} U_A }{(-\\nu_A) k \\frac{1-U_A}{1 + \\epsilon_A x_{A,0} U_A}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vr= 140.25L\n",
      "tau= 7.79168min\n"
     ]
    }
   ],
   "source": [
    "vdot0 = 9/0.5 # L/min\n",
    "vr = 0.667/(1-0.667)*(1+(+3-1)/(-(-1))*0.667)*vdot0/(\n",
    "    -(-1.0)*0.6) # L\n",
    "tau = vr/vdot0\n",
    "print('Vr= ' + '{0:g}'.format(vr) + 'L')\n",
    "print('tau= ' + '{0:g}'.format(tau) + 'min')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ü 5.5\n",
    "$4 PH_3(g) \\rightarrow P_4(g) + 6 H_2(g)$\n",
    "\n",
    "A: $PH_3(g)$\n",
    "\n",
    "$-r_{PH_3} = \\nu_{PH_3} r_1 = 10 h^{-1} C_{PH_3}$\n",
    "\n",
    "Hagen: $\\dot{n_A} = (\\dot{n_A} + d \\dot{n_A}) - r_A dV$\n",
    "\n",
    "Vorgeschlagen: $\\dot{n_A} = (\\dot{n_A} + d \\dot{n_A}) + r_A dV$ \n",
    "\n",
    "$\\hspace{2cm} 0 = (\\{\\text{Zulaufstrom}\\} - \\{\\text{Auslassstrom}\\}) + \\{\\text{Durch chemische Reaktion verwendete oder gebildete Stoffmengenstrom}\\}$\n",
    "\n",
    "$\\frac{d \\dot{n_A}}{dV} = \\nu_{A1} r_1$\n",
    "\n",
    "Sonst wäre Abbildung 5-8 gar nicht möglich, denn die Steigerung $\\frac{d U_A}{dV}$ wäre negativ.\n",
    "\n",
    "$\\frac{d \\dot{n_A}}{dV} = \\frac{d \\dot{n}_{A,0}}{dV}(1-U_A) = -\\dot{n}_{A,0}\\frac{d U_A}{dV} = - 10 h^{-1} c_A$\n",
    "\n",
    "$c_A = \\dot{n_A}/\\dot{V} = (\\dot{n}_{A,0}/\\dot{V}) \\times (1-U_A) = (\\dot{n}_{A,0}/\\dot{V_0}) \\times \\frac{1-U_A}{1+\\epsilon_A x_{A,0} U_A}$ \n",
    "\n",
    "$\\int_{0}^{V_R}dV = V_R = \\int_{0}^{U_A} \\frac{\\dot{n}_{A,0}}{k_1 c_{A,0}} \\times \\frac{1+\\epsilon_A x_{A,0} U_A}{1-U_A} dU_A $\n",
    "\n",
    "$= \\frac{\\dot{n}_{A,0}}{k_1 c_{A,0}} \\times(-(1+\\epsilon_A x_{A,0})ln(1-U_A)-\\epsilon_A x_{A,0}U_A)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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      "text/latex": [
       "$$\\frac{a x + c}{b x + d} = - \\frac{a d}{b \\left(b x + 1\\right)} + \\frac{b x \\frac{a}{b}}{b x + 1} + \\frac{c}{b x + d} + \\frac{a d}{b \\left(b x + 1\\right)} = \\frac{a}{b} + \\frac{- \\frac{a d}{b} + c}{b x + d}$$"
      ],
      "text/plain": [
       "                               a                                  a⋅d    \n",
       "                           b⋅x⋅─                                - ─── + c\n",
       "a⋅x + c         a⋅d            b       c          a⋅d       a      b     \n",
       "─────── = - ─────────── + ─────── + ─────── + ─────────── = ─ + ─────────\n",
       "b⋅x + d     b⋅(b⋅x + 1)   b⋅x + 1   b⋅x + d   b⋅(b⋅x + 1)   b    b⋅x + d "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "simplify back\n"
     ]
    },
    {
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      "text/latex": [
       "$$\\frac{a}{b} + \\frac{- \\frac{a d}{b} + c}{b x + d} = \\frac{a x + c}{b x + d}$$"
      ],
      "text/plain": [
       "      a⋅d              \n",
       "    - ─── + c          \n",
       "a      b        a⋅x + c\n",
       "─ + ───────── = ───────\n",
       "b    b⋅x + d    b⋅x + d"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\frac{\\partial}{\\partial x}\\left(\\frac{a x}{b} + \\frac{1}{b} \\left(- \\frac{a d}{b} + c\\right) \\log{\\left (b x + d \\right )}\\right) = \\frac{a x + c}{b x + d}$$"
      ],
      "text/plain": [
       "  ⎛      ⎛  a⋅d    ⎞             ⎞          \n",
       "  ⎜      ⎜- ─── + c⎟⋅log(b⋅x + d)⎟          \n",
       "∂ ⎜a⋅x   ⎝   b     ⎠             ⎟   a⋅x + c\n",
       "──⎜─── + ────────────────────────⎟ = ───────\n",
       "∂x⎝ b               b            ⎠   b⋅x + d"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import sympy\n",
    "from IPython.display import display\n",
    "from sympy import UnevaluatedExpr\n",
    "from sympy import oo\n",
    "sympy.init_printing()\n",
    "x, a, b, c, d = sympy.symbols('x, a, b, c, d')\n",
    "display(sympy.Eq(sympy.Eq(\n",
    "    (c+a*x)/(d+b*x), c/(d+b*x) + UnevaluatedExpr(\n",
    "        a/b)*b*x/(1+b*x) + UnevaluatedExpr(\n",
    "        a/b*d/(1+b*x) \n",
    "        )-a/b*d/(1+b*x)), (c-a/b*d)/(d+b*x) + a/b\n",
    "))\n",
    "print('simplify back')\n",
    "display(sympy.Eq((c-a/b*d)/(d+b*x) + a/b, \n",
    "                 sympy.simplify((c-a/b*d)/(d+b*x) + a/b)))\n",
    "display(sympy.Eq(\n",
    "    UnevaluatedExpr(sympy.Derivative(\n",
    "        (c-a/b*d)*1/b*sympy.log(d+b*x)+a/b*x,x)),\n",
    "    sympy.simplify(sympy.diff(\n",
    "        (c-a/b*d)*1/b*sympy.log(d+b*x)+a/b*x,x))\n",
    "))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vr= 7.39804L\n"
     ]
    }
   ],
   "source": [
    "ca0 = 4.6*1e5/101325.0/(0.08207*(650+273.15)) # mol(A)/L\n",
    "ua = 0.80\n",
    "nadot0 = 2.0 # mol(A)/h\n",
    "k1 = 10.0 # h^-1\n",
    "eps_a = (-4+1+6)/(-(-4.0))\n",
    "vr = nadot0/(k1*ca0)*(\n",
    "    -(1+eps_a*1.0)*np.log(1-ua)-eps_a*1.0*ua)\n",
    "print('Vr= ' + '{0:g}'.format(vr) + 'L')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ü 5.6\n",
    "Gasphasencracking bei 800°C, 6 bar:\n",
    "\n",
    "$C_2 H_6 \\rightarrow C_2H_4 + H_2$\n",
    "\n",
    "A: $C_2H_6$\n",
    "\n",
    "B: $C_2H_4$\n",
    "\n",
    "Bedingungen: Reaktion 1. Ordnung, k = $3,07 s^{–1}$ (800 °C). Es sollen 300000 t Ethylen/Jahr (1 Jahr = 300 Tage) hergestellt werden bei einem Umsatz von Ethan= 0,80.\n",
    "Berechne das notwendige Volumen eines Strömungsrohrreaktors für die genannte Reaktion; es gilt die ideale Gasgleichung.\n",
    "\n",
    "**Lösung**\n",
    "\n",
    "$Z=\\frac{P V}{n R T}$\n",
    "\n",
    "$\\frac{\\dot{V}}{\\dot{V_0}}=\\left(\\frac{\\dot{n}}{\\dot{n_0}}\\right)\\left(\\frac{T}{T_0}\\right)\\left(\\frac{P_0}{P}\\right)\\left(\\frac{Z}{Z_0}\\right)$\n",
    "\n",
    "$\\frac{\\dot n}{\\dot n_0}=\\frac{n_0 + (\\sum_i{\\nu_i})\\xi_1}{n_0} = 1 + \\frac{(\\sum_i{\\nu_i})\\xi_1}{n_0}$\n",
    "\n",
    "$Z=1$, isothermisch, isobarisch\n",
    "\n",
    "$\\frac{\\dot{V}}{\\dot{V_0}}=\\left(\\frac{\\dot{n}}{\\dot{n_0}}\\right)=1+(\\sum_i{\\nu_i})\\left(\\frac{\\dot{n}_B - \\dot{n}_{B,0}}{\\nu_B \\dot n_0}\\right)$\n",
    "\n",
    "$\\frac{d \\dot{n_B}}{dV} = \\nu_{B} r_1 = \\nu_{B} k_1 c_A$\n",
    "\n",
    "$c_A$ als funktion des Stoffmengenstromes $\\dot n_B$\n",
    "\n",
    "$c_A = \\frac{\\dot n_A}{\\dot V} = \\frac{p_A}{R T}$, \n",
    "$c_B = \\frac{\\dot n_B}{\\dot V} = \\frac{p_B}{R T}$\n",
    "\n",
    "$c_A + c_B + c_C = \\frac{p_A}{R T} + \\frac{p_B}{R T} + \\frac{p_C}{R T} = \\frac{P}{R T}$\n",
    "\n",
    "$c_A = \\frac{P}{R T} - \\frac{\\dot n_B}{\\dot V} - \\frac{\\dot n_C}{\\dot V}=\\frac{P}{R T} - \\frac{(\\dot {n}_B+\\dot {n}_C)}{\\dot V_0}\\times \\frac{1}{1+(\\sum_i{\\nu_i})\\left(\\frac{\\dot{n}_B - \\dot{n}_{B,0}}{\\nu_B \\dot n_0}\\right)}$\n",
    "\n",
    "Nach Ersatz:\n",
    "\n",
    "$\\frac{d \\dot{n_B}}{dV} = \\nu_{B} k_1 \\frac{P}{R T} -  \\nu_{B} k_1\\frac{\\dot {n}_B+\\dot {n}_C}{\\dot V_0}\\times \\frac{1}{1+(\\sum_i{\\nu_i})\\left(\\frac{\\dot{n}_B - \\dot{n}_{B,0}}{\\nu_B \\dot n_0}\\right)}$\n",
    "\n",
    "$V_R = \\int_{0}^{V_R} 1 dV = \\int_{0}^{\\dot {n}_B} \\frac{1 - \\frac{\\sum_i \\nu_i}{\\nu_B}\\frac{\\dot {n}_{B,0}}{\\dot {n}_0}+\\frac{\\sum_i \\nu_i}{\\nu_B}\\frac{\\dot {n}_{B}}{\\dot {n}_0}}{\\nu_B k_1 \\frac{P}{RT} \\times \\left(1+\\frac{\\sum_i \\nu_i}{\\nu_B}\\frac{\\dot {n}_{B}}{\\dot {n}_0}-\\frac{\\sum_i \\nu_i}{\\nu_B}\\frac{\\dot {n}_{B,0}}{\\dot {n}_0} -\\frac{RT}{P V_0}\\dot{n}_B -\\frac{RT}{P V_0}\\dot{n}_C  \\right) }d \\dot {n}_{B}$\n",
    "\n",
    "$V_R = \\frac{R T}{P}\\frac{1}{\\nu_B k_1} \\int_{0}^{\\dot {n}_B} \\frac{\\left(1 - \\frac{\\sum_i \\nu_i}{\\nu_B}\\frac{\\dot {n}_{B,0}}{\\dot {n}_0}\\right)+\\frac{\\sum_i \\nu_i}{\\nu_B}\\frac{1}{\\dot {n}_0}\\dot {n}_{B}}{\\left(1-\\frac{\\sum_i \\nu_i}{\\nu_B}\\frac{\\dot {n}_{B,0}}{\\dot {n}_0}\\right)-\\left(1-\\frac{\\sum_i \\nu_i}{\\nu_B} \\right)\\frac{1}{\\dot {n}_0} \\dot{n}_B - \\frac{1}{\\dot {n}_0} \\dot{n}_C }d \\dot {n}_{B}$\n",
    "\n",
    "$\\frac{\\sum_i \\nu_i}{\\nu_B}=\\frac{-1+1+1}{+1} = 1$\n",
    "\n",
    "$\\dot {n}_{B,0}=0$\n",
    "\n",
    "$\\dot {n}_{C,0}=0$\n",
    "\n",
    "$\\dot {n}_0=\\dot {n}_{A,0}+\\dot {n}_{B,0}+\\dot {n}_{C,0}=\\dot {n}_{A0}$\n",
    "\n",
    "$U_A = \\frac{\\dot {n}_{A,0}-\\dot{n}_A}{\\dot{n}_{A,0}} =\\frac{\\dot {n}_{A,0}-\\dot{n}_{A,0} -\\nu_A \\xi_1 }{\\dot{n}_{A,0}} =  \\frac{(-\\nu_A)}{\\nu_B}\\frac{\\dot {n}_B - \\dot {n}_{B,0}}{\\dot{n}_{A,0}}$\n",
    "\n",
    "$\\Longrightarrow \\dot{n}_{A,0} = \\dot{n}_{0} = \\frac{(-\\nu_A)}{\\nu_B}\\frac{\\dot {n}_B -0}{U_A}$\n",
    "\n",
    "$\\dot {n}_C=\\dot {n}_{C,0} + \\nu_C \\xi_1$\n",
    "\n",
    "$\\dot {n}_B=\\dot {n}_{B,0} + \\nu_B \\xi_1$\n",
    "\n",
    "$\\Longrightarrow \\dot {n}_C=\\frac{\\nu_C}{\\nu_B} \\dot {n}_B$\n",
    "\n",
    "$V_R = \\frac{R T}{P}\\frac{1}{\\nu_B k_1} \\int_{0}^{\\dot {n}_B} \\frac{1+\\frac{\\sum_i \\nu_i}{\\nu_B}\\frac{1}{\\dot {n}_0}\\dot {n}_{B}}{1 - \\frac{\\nu_C}{\\nu_B}\\frac{1}{\\dot {n}_0} \\dot {n}_B }d \\dot {n}_{B} = \\frac{R T}{P}\\frac{1}{\\nu_B k_1} \\left( -\\frac{\\sum_i \\nu_i}{\\nu_C} \\dot {n}_B - \\dot {n}_0 \\frac{\\nu_B}{\\nu_C}(1+\\frac{\\sum_i \\nu_i}{\\nu_C} ) \\times ln(1-\\frac{\\nu_C}{\\nu_B}\\frac{1}{\\dot {n}_0} \\dot {n}_B) \\right)$\n",
    "\n",
    "$V_R = \\frac{R T}{P}\\frac{\\dot {n}_B}{\\nu_B k_1} \\left( -\\frac{\\sum_i \\nu_i}{\\nu_C}  - \\frac{(-\\nu_A)}{\\nu_C} \\frac{1}{U_A}(1+\\frac{\\sum_i \\nu_i}{\\nu_C} ) \\times ln(1-\\frac{\\nu_C}{(-\\nu_A)}U_A) \\right)$\n",
    "\n",
    "$V_R =\\frac{R T}{P}\\frac{\\dot {n}_B}{\\nu_B k_1} \\left( -1  - \\frac{1}{U_A}(1+1) \\times ln(1-U_A) \\right)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vr = 6053.86L\n",
      "ca0 = na/V = P/RT = 0.0672482mol/L\n",
      "na0 = nb/U_A nua/nub = 516.7mol/L\n"
     ]
    }
   ],
   "source": [
    "nb = 300000.0 * 1e6 /(12.0*2+1.0*4) / (300.*24.*60.*60.) # molB/s\n",
    "ua = 0.80\n",
    "p = 6.0 # bar\n",
    "r = 8.314/100.0 # L kPa/(mol K) * 1bar/(100kPa)\n",
    "t = 800 + 273.15 # K\n",
    "k1 = 3.07 # s^-1\n",
    "nub = +1.\n",
    "nua = -1.\n",
    "nu = +1.+1.-1.\n",
    "vr = nb * r * t / (p * k1 * nub) * (\n",
    "    -1 - 1/ua * (1+1) * np.log( 1 - ua)\n",
    ")\n",
    "print ('Vr = ' + '{0:g}'.format(vr) + 'L')\n",
    "print ('ca0 = na/V = P/RT = ' + '{0:g}'.format(p / (r * t)) + 'mol/L')\n",
    "print ('na0 = nb/U_A nua/nub = ' + '{0:g}'.format(nb/ua) + 'mol/L')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ü 5.7 [5]\n",
    "\n",
    "Die irreversible Zersetzung von Di-tert.-Butylperoxid wird in einem isotherm betriebenen Strömungsrohr ohne Druckverlust betrieben; $A \\rightarrow B + 2 C$. Der Einsatzstrom besteht aus  reinem  Peroxid und inertem  Stickstoff.  Das Reaktorvolumen ist  200  L, der Eintrittsstrom beträgt 10  L/min.  Die  Reaktion verläuft bezüglich A nach  1.  Ordnung, $k = 0,08 min^{-1}$.\n",
    "\n",
    "a)  Ermittle  den  Umsatz  als  Funktion  des  Reaktorvolumens  für  einen  Zulaufstrom von reinem  A mit einer  Konzentration von  1,0 mol/L.  Vergleiche den \n",
    "Umsatzverlauf,  wenn  der  Zulaufstrom  nur  5 %  A  enthält,  der  Rest  besteht aus  Stickstoff.\n",
    "\n",
    "b)  Vergleiche  die  Ergebnisse  für  eine  Reaktion  $3A  \\rightarrow B$  mit  der  selben \n",
    "Geschwindigkeitskonstante, alle anderen Bedingungen bleiben gleich."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Lösung**\n",
    "\n",
    "$\\frac{d \\dot {n}_A}{d V} = -k_1 c_A$\n",
    "\n",
    "$\\dot {n}_A = \\dot {n}_{A, 0} (1-U_A) = n_{A,0} + \\nu_A \\xi_1$\n",
    "\n",
    "$\\dot {V} = \\frac{R T}{P} \\sum_i{n_i} =  \\frac{R T}{P} \\sum_i(n_{i,0} + \\nu_{i,1} \\xi_1) = \\frac{R T}{P} (n_0 + \\frac{\\sum_i(\\nu_{i,1})}{-\\nu_A} U_A n_{A,0} ) =\\dot {V}_0 (1 + \\frac{\\sum_i(\\nu_{i,1})}{-\\nu_A} x_{A,0} U_A )$\n",
    "\n",
    "$\\epsilon_A \\equiv \\frac{\\sum_i(\\nu_{i,1})}{-\\nu_A}$\n",
    "\n",
    "$-\\frac{d U_A}{d V} = -k_1 \\frac{\\dot {n}_A}{\\dot {V}}  = \\frac{\\dot {n}_{A,0}}{\\dot {V}_0}\\frac{1 - U_A}{1 + \\epsilon_A x_{A,0} U_A}$\n",
    "\n",
    "$V_R = \\frac{\\dot {V}_0}{k_1}(-\\epsilon_A x_{A,0} U_A - (1+\\epsilon_A x_{A,0})ln(1-U_A))$\n",
    "\n",
    "$0 = k_1\\frac{V_R}{\\dot {V}_0} +\\epsilon_A x_{A,0} U_A + (1+\\epsilon_A x_{A,0})ln(1-U_A)$ ... solve for UA\n",
    "\n",
    "$A \\rightarrow B + 2C$\n",
    "\n",
    "$\\epsilon_A = (-1+1+2)/(-(-1)) = +2$\n",
    "\n",
    "$3A \\rightarrow B$\n",
    "\n",
    "$\\epsilon_A = (-3+1)/(-(-3)) = -2/3$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100% A\n",
      "UA = 0.609151\n",
      "5% A\n",
      "UA = 0.782528\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1645bd3b400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import root\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "xa0 = 1.\n",
    "k1 = 0.08 # min^-1\n",
    "v0 = 10. # L/min\n",
    "vr = 200 # L\n",
    "def ua(vr, epsa, xa0):\n",
    "    return root(lambda ua_var: \n",
    "        vr / v0 * k1 + \n",
    "        epsa * xa0 * ua_var + \n",
    "        (1 + epsa * xa0) * np.log(1 - ua_var),\n",
    "        0.99\n",
    "    ).x\n",
    "ua = np.vectorize(ua) # Vektorisieren\n",
    "print ('100% A')\n",
    "print ('UA = ' + '{0:g}'.format(\n",
    "    ua(vr, epsa=(-1. +2. + 1.)/(-(-1.)), xa0=1.).item()\n",
    "))\n",
    "\n",
    "xa0 = 0.05\n",
    "print ('5% A')\n",
    "print ('UA = ' + '{0:g}'.format(\n",
    "    ua(vr, epsa=-1. +2. + 1., xa0=0.05).item()\n",
    "))\n",
    "\n",
    "vr = np.array(range(0,200,1))\n",
    "plt.subplots(nrows=2, ncols=1)\n",
    "plt.subplot(2,1,1)\n",
    "plt.plot(\n",
    "    vr, ua(vr, epsa=(-1. + 2. + 1.)/(-(-1.)), xa0=1.), '-.',\n",
    "    vr, ua(vr, epsa=(-1. + 2. + 1.)/(-(-1.)), xa0=0.05), '-'\n",
    ")\n",
    "plt.xlabel('Vr, L')\n",
    "plt.ylabel('UA')\n",
    "plt.legend(['reines A', 'mit Stickstoff'])\n",
    "plt.title('$A \\\\rightarrow B + 2 C$')\n",
    "plt.subplot(2,1,2)\n",
    "plt.plot(\n",
    "    vr, ua(vr, epsa=(-3. + 1.)/(-(-3.)), xa0=1.), '-.',\n",
    "    vr, ua(vr, epsa=(-3. + 1.)/(-(-3.)), xa0=0.05), '-'\n",
    ")\n",
    "plt.xlabel('Vr, L')\n",
    "plt.ylabel('UA')\n",
    "plt.legend(['reines A', 'mit Stickstoff'])\n",
    "plt.text(0.5,0.5, '$3A \\\\rightarrow B$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Fazit**\n",
    "\n",
    "a) Bezüglich der Reaktion, wobei eine höhere Stoffmenge an Produkt hergestellt wird, als der Reagenzienkonsum ist es bevorzugt, ein inertes Komponent einzuführen. Denn somit steigt der Gesamtdruck, und somit die Konzentration und folglich die Reaktionsgeschwindigkeit.\n",
    "\n",
    "b) Bei der Reaktion, die eine niedrigere Produktstoffmege herstellt, als sie verbraucht ist es begünstigt, keine zusätzlichen Komponente einzuführen. Denn die Reaktion selbst erniedrigt den Gesamtdruck, und somit die Konzentratrion und infolgedessen die Reaktionsgeschwindigkeit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ü 5.8\n",
    "Die  Gasphasendehydrierung von  Benzol  B  zu  Diphenyl  D und weiter zu Triphenyl T wird  in  einem  isotherm  betriebenen  Strömungsrohr  durchgeführt.  Ziel  ist,  die \n",
    "Produktion  von  D  zu  maximieren  und  die  Weiterreaktion  zu  T zu  unterdrücken. \n",
    "Die Reaktion wird bei Normaldruck durchgeführt.\n",
    "\n",
    "$\\begin{array}{ccccc}\n",
    "    2 C_6H_6 & & \\overset{k_1}{\\longrightarrow} &  C_{12}H_{10}+& H_2\\\\\n",
    "    B & & & D & H\\\\\n",
    "    C_6H_6 +& C_{12}H_{10} & \\overset{k_2}{\\longrightarrow} & C_{18}H_{14} +& H_2\\\\\n",
    "    B & D & & T & H\\\\\n",
    "\\end{array}$\n",
    "\n",
    "Die Geschwindigkeitsgleichungen lauten wie folgt:\n",
    "\n",
    "$r_1  = 14,96 \\cdot 10^6 e^{-15200/T} \\left(p_B^2- \\frac{p_D p_H}{K_1} \\right)   kg \\cdot h^{-1} \\cdot L^{-1}$\n",
    "\n",
    "$r_2 = -8,67 \\cdot 10^6 e^{-15200/T}\\left(p_B p_D - \\frac{p_T p_H}{K_2}\\right)$\n",
    "\n",
    "$K_1 = 0,312$\n",
    "\n",
    "$K_2 = 0,480$\n",
    "\n",
    "1.  Studiere den Effekt der Raumzeit $\\tau$ auf die Umsätze $U_1$ und  $U_2$ und ermittle die Stoffströme im Reaktor.\n",
    "2.  Bestimme die Reaktionsgeschwindigkeiten $r_1$ und $r_2$ als Funktion der Raumzeit $\\tau$.\n",
    "\n",
    "**Lösung**\n",
    "\n",
    "Raumzeit (hydrodynamische Verweilzeit) $\\tau = \\frac{V_R}{\\dot {V}}$\n",
    "\n",
    "Billanz\n",
    "\n",
    "$\\frac{d \\dot{n}_B}{d V} = \\nu_{B,1}r_1+\\nu_{B,2}r_2 = -r_1 - r_2$\n",
    "\n",
    "Als Funktion der Raumzeit und des Partialdrucks $n_B = \\frac{p_B \\dot {V}}{R T}$:\n",
    "\n",
    "$\\frac{d \\dot{n}_B}{d V} = \\frac{1}{R T}\\frac{d p_B \\dot {V}}{d (V)} =\\frac{1}{R T}\\frac{d p_B }{d (V/\\dot {V})}= \\frac{1}{R T}\\frac{d p_B }{d \\tau}$\n",
    "\n",
    "${\\boldsymbol \\nu} = \\left( \n",
    "\\begin{array}{cccc}\n",
    "\\nu_{B,1} & \\nu_{D,1} & \\nu_{T,1} & \\nu_{H,1} \\\\\n",
    "\\nu_{B,2} & \\nu_{D,2} & \\nu_{T,2} & \\nu_{H,2}\\\\\n",
    "\\end{array}\n",
    "\\right) = \n",
    "\\left( \n",
    "\\begin{array}{cccc}\n",
    "-2 & +1 & 0 & +1 \\\\\n",
    "-1 & -1 & +1 & +1\\\\\n",
    "\\end{array}\n",
    "\\right)$\n",
    "\n",
    "$\\frac{1}{R T}\\frac{d {\\bf p}}{d \\tau} = {\\bf \\nu} {\\bf r}$\n",
    "\n",
    "$\\frac{1}{R T}\\frac{d p_B}{d \\tau} = -2 k_1 e^{-15200/T}\\left(p_B^2- \\frac{p_D p_H}{K_1} \\right) - k_2 e^{-15200/T}\\left(p_B p_D - \\frac{p_T p_H}{K_2}\\right)$\n",
    "\n",
    "$\\frac{1}{R T}\\frac{d p_D}{d \\tau} = + k_1 e^{-15200/T}\\left(p_B^2- \\frac{p_D p_H}{K_1} \\right) - k_2 e^{-15200/T}\\left(p_B p_D - \\frac{p_T p_H}{K_2}\\right)$\n",
    "\n",
    "$\\frac{1}{R T}\\frac{d p_T}{d \\tau} = + k_2 e^{-15200/T}\\left(p_B p_D - \\frac{p_T p_H}{K_2}\\right)$\n",
    "\n",
    "$\\frac{1}{R T}\\frac{d p_H}{d \\tau} = + k_1 e^{-15200/T}\\left(p_B^2- \\frac{p_D p_H}{K_1} \\right) + k_2 e^{-15200/T}\\left(p_B p_D - \\frac{p_T p_H}{K_2}\\right)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1645e7af4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.integrate import odeint\n",
    "t = 1033. # K\n",
    "r = 8.314/1000. # J / (mol K) [=] 8.314 kPa / (mol K)\n",
    "# Angeblich sollen die Einheiten der Geschwindigkeitskonstante \n",
    "# kg h^{-1} L^{-1}, was aber nicht Sinn ergibt, denn sind die kg\n",
    "# in der zweiten Konstante auch kg? Wenn so, sind es kg von B oder\n",
    "# D? Es wäre verständlicher, mit Einheiten kgmol h^{-1} L^{-1}\n",
    "k1 = 14.96E+06 * np.exp(15200./t) # kgmol h^{-1} L^{-1}\n",
    "k2 = -8.67E+06 * np.exp(15200./t) # kgmol h^{-1} L^{-1}\n",
    "kp1 = 0.312 # \n",
    "kp2 = 0.480 # \n",
    "def eq_set(y, t):\n",
    "    pb, pd, pt, ph = y\n",
    "    res = np.empty(4, dtype=np.float)\n",
    "    res[0] = r * t * (\n",
    "        -2 * k1 * (pb**2 - pd*ph/kp1) + \n",
    "        -1 * k2 * (pb*pd - pt*ph/kp2))\n",
    "    res[1] = r * t * (\n",
    "        +1 * k1 * (pb**2 - pd*ph/kp1) +\n",
    "        -1 * k2 * (pb*pd - pt*ph/kp2))\n",
    "    res[2] = r * t * (\n",
    "        +1 * k2 * (pb*pd - pt*ph/kp2))\n",
    "    res[3] = r * t * (\n",
    "        +1 * k1 * (pb**2 - pd*ph/kp1) + \n",
    "        +1 * k2 * (pb*pd - pt*ph/kp2))\n",
    "    return res\n",
    "t = np.arange(0, 0.00001, 0.00000001)\n",
    "y0 = np.array([1.0, 0, 0, 0])\n",
    "y = odeint(eq_set, y0, t)\n",
    "plt.plot(t, y)\n",
    "plt.legend(['B', 'D', 'T', 'H'])\n",
    "plt.xlabel('Raumzeit, $\\\\tau$' + \"'\")\n",
    "plt.ylabel('$p_i$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ü 5.9\n",
    "Eine  Reaktion 1. Ordnung mit $\\epsilon_A=0$ wird in einem  Kreislaufreaktor durchgeführt, $k \\tau = 5$. Welche Umsätze resultieren für ein Kreislaufverhältnis von 0, 5, 10 und $\\infty$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"rvm_001.jpg\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Lösung**\n",
    "\n",
    "Raumzeit (hydrodynamische Verweilzeit). Sie gibt definitionsgemäß das Verhältnis des Reaktionsvolumens zum volumetrischen **Zulauf**strom an.\n",
    "\n",
    "$\\tau = \\frac{V_R}{\\dot V_0}$\n",
    "\n",
    "Reaktion 1. Ordnung\n",
    "\n",
    "$A \\rightarrow Produkte...\\hspace{10mm} r_1 = k c_A$\n",
    "\n",
    "$\\nu_{A1}=-1$\n",
    "\n",
    "Stoffbilanz am Reaktor Ausgangsstrom:\n",
    "\n",
    "$\\frac{d \\dot{n}_{A,2}}{d V} = \\nu_{A1}r_1$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Allgemeiner Umsatz*\n",
    "\n",
    "$U_A = \\frac{\\dot n_{A,0} - \\dot n_A}{\\dot n_{A,0}}=1-\\frac{\\dot n_A}{\\dot n_{A,0}}=1-\\left(\\frac{c_A}{c_{A,0}}\\right)\\left(\\frac{\\dot V}{\\dot V_0}\\right)$\n",
    "\n",
    "$\\rightarrow \\dot n_A = \\dot n_{A0}(1-U_A)$\n",
    "\n",
    "*Allgemeine Stoffbilanzen*\n",
    "\n",
    "$\\begin{array}{ll}\n",
    "\\dot n_A &= \\dot n_{A,0} + \\nu_{A1}\\xi_1 \\hspace{10mm} \\rightarrow \\xi_1 = \\frac{\\dot n_A}{(-\\nu_{A1})}U_A\\\\\n",
    "\\dot n &= \\dot n_0 + (\\sum_j \\nu_{j1})\\xi_1\\\\\n",
    "&= \\dot n_0 + \\left(\\frac{\\sum_j \\nu_{j1}}{-\\nu_A}\\right)\\dot n_{A0} U_A\\\\\n",
    "&= \\dot n_0 \\left(1+\\left(\\frac{\\sum_j \\nu_{j1}}{-\\nu_A}\\right) x_{A0} U_A \\right)\\\\\n",
    "&= \\dot n_0 \\left(1+\\epsilon_A x_{A0} U_A \\right)\\\\\n",
    "\\end{array}$\n",
    "\n",
    "*Innerliche Stoffblianzen*\n",
    "\n",
    "$\\begin{array}{ll}\n",
    "\\dot n_{A2} &= \\dot n_A + \\dot n_{Ar}\\\\\n",
    "&= (R+1)\\dot n_A\\\\\n",
    "\\dot n_{A1} &= \\dot n_{A0} + \\dot n_{Ar}\\\\\n",
    "\\end{array}$\n",
    "\n",
    "*Volumenänderung*\n",
    "\n",
    "$\\frac{P \\dot V}{\\dot n R T}=Z$\n",
    "\n",
    "$\\frac{P \\dot V}{Z R T} = \\frac{P_0 \\dot V_0}{Z_0 R T_0}\\left(1+\\epsilon_A x_{A0} U_A \\right)$\n",
    "\n",
    "$\\require{cancel}$\n",
    "$\\dot V = \\dot V_0 \\left(1+\\epsilon_A x_{A0} U_A \\right)\\times \\cancelto{1}{ \\frac{P_0}{P}}\\cancelto{1}{\\frac{T}{T_0}}\\cancelto{1}{\\frac{Z}{Z_0}}$ (I. G.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ACS4+AkjQMQBIEAwAEgQDgATBACBBMABIEAwAEgQDgATBACBBMABIEAwAEgQDgATBACBBMABIEAwAEgQDgATBACBBMABIEAwAEgQDgATBACBBMABIEAwAEgQDgMT/AW34wvEqdFKdAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1645e7fa550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "patch1 = matplotlib.patches.Circle(\n",
    "    [0.5,0.5],0.05\n",
    ")\n",
    "patch2 = matplotlib.patches.Rectangle(\n",
    "    [0.3,0.3],0.4, 0.4, alpha=0.5, \n",
    "    fill=False, edgecolor='black',\n",
    "    linestyle = '--'\n",
    ")\n",
    "arrow1 = matplotlib.patches.Arrow(\n",
    "    0, 0.5,0.45,0, width=0.05,\n",
    "    color='black'\n",
    ")\n",
    "arrow2 = matplotlib.patches.Arrow(\n",
    "    0.55, 0.5,0.45,0, width=0.05,\n",
    "    color='black'\n",
    ")\n",
    "line1 = matplotlib.lines.Line2D(\n",
    "    [0.5,0.5], [0,0.45],\n",
    "    linestyle='--', color='black'\n",
    ")\n",
    "text1 = matplotlib.text.Text(\n",
    "    0, 0.45, '$n_{A0}$\\n$V_0$\\n$U_A=0$'\n",
    ")\n",
    "text2 = matplotlib.text.Text(\n",
    "    0.8, 0.45, '$n_{A1}$\\n$V_1$\\n$U_{A1}$'\n",
    ")\n",
    "for artist in [\n",
    "    patch1,patch2,arrow1,arrow2,\n",
    "    line1,text1,text2\n",
    "]:\n",
    "    ax.add_artist(artist)\n",
    "ax.set_frame_on(False)\n",
    "ax.set_axis_off()\n",
    "ax.set_aspect(1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Umsatz am Knotenpunkt # 1.\n",
    "\n",
    "In folgender Weise wird der Umsatz 1 definiert. Definitionsgemäß nimmt er nur den Speisestrom und den Reaktoreneintrittstrom in Acht, ohne irgendeiner Absicht auf den Rücklaufstrom.\n",
    "\n",
    "$U_{A1} = \\frac{\\dot n_{A0} - \\dot n_{A1}}{\\dot n_{A0}} = 1 - \\frac{\\dot n_{A1}}{\\dot n_{A0}} = 1- \\frac{c_{A1}}{c_{A0}} \\left(\\frac{\\dot V_1}{\\dot V_0} \\right)$\n",
    "\n",
    "$\\dot V_1 = \\dot V_0(1+\\epsilon_A x_{A0}U_{A1})$\n",
    "\n",
    "$U_{A1} = 1-\\frac{c_{A1}}{c_{A0}}(1+\\epsilon_A x_{A0}U_{A1})$ \n",
    "\n",
    "$\\begin{array}{lll}\\Rightarrow & U_{A1} & = \\frac{1-c_{A1}/c_{A0}}{1+\\epsilon_A x_{A0}c_{A1}/c_{A0}}\\\\ & c_{A1} & =\\left(\\frac{1-U_{A1}}{1+\\epsilon_A x_{A0}U_{A1}}\\right)c_{A0}\\end{array}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1645e8885f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "patch1 = matplotlib.patches.Circle(\n",
    "    [0.5,0.5],0.05\n",
    ")\n",
    "patch2 = matplotlib.patches.Rectangle(\n",
    "    [0.3,0.3],0.4, 0.4, alpha=0.5, \n",
    "    fill=False, edgecolor='black',\n",
    "    linestyle = '--'\n",
    ")\n",
    "arrow1 = matplotlib.patches.Arrow(\n",
    "    0, 0.5,0.45,0, width=0.05,\n",
    "    color='black'\n",
    ")\n",
    "arrow2 = matplotlib.patches.Arrow(\n",
    "    0.55, 0.5,0.45,0, width=0.05,\n",
    "    color='black'\n",
    ")\n",
    "arrow3 = matplotlib.patches.Arrow(\n",
    "    0.5, 0.0, 0,0.45, width=0.05,\n",
    "    color='black'\n",
    ")\n",
    "text1 = matplotlib.text.Text(\n",
    "    0, 0.45, '$n_{A0}$\\n$V_0$\\n$U_A=0$'\n",
    ")\n",
    "text2 = matplotlib.text.Text(\n",
    "    0.8, 0.45, '$n_{A1}$\\n$V_1$\\n$U_{A1}$'\n",
    ")\n",
    "text3 = matplotlib.text.Text(\n",
    "    0.55, 0.1, '$n_{Ar}$\\n$V_r$'\n",
    ")\n",
    "for artist in [\n",
    "    patch1,patch2,arrow1,arrow2,\n",
    "    arrow3,text1,text2,text3\n",
    "]:\n",
    "    ax.add_artist(artist)\n",
    "ax.set_frame_on(False)\n",
    "ax.set_axis_off()\n",
    "ax.set_aspect(1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Konzentration am Knotenpunkt # 1.\n",
    "\n",
    "$c_{A1} = \\frac{\\dot n_{A0} + \\dot n_{A1}}{\\dot V_0 + \\dot V_{ar}} = \\frac{\\dot n_{A0} + R \\dot n_{A0}(1-U_A)}{\\dot V_0  + R \\dot V_0 (1+\\epsilon_A x_{A0}U_A)}=c_{A0}\\left(\\frac{1 + R -U_A R}{1 + R+\\epsilon_A x_{A0}U_A R} \\right)$\n",
    "\n",
    "$\\left(\\frac{1-U_{A1}}{1+\\epsilon_A x_{A0}U_{A1}}\\right)c_{A0}=c_{A0}\\left(\\frac{1 + R -U_A R}{1 + R+\\epsilon_A x_{A0}U_A R} \\right)$\n",
    "\n",
    "$\\Rightarrow U_A \\frac{R}{R+1} = U_{A1}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Mathematisches Modell*\n",
    "\n",
    "$\\frac{d \\dot{n}_{A,2}}{d V} = \\nu_{A1}r_1$\n",
    "\n",
    "$\\begin{array}{ll}\n",
    "\\frac{d \\dot{n}_{A,2}}{d V} &= \\frac{d (R+1)c_A \\dot V}{d V} = \\frac{d }{d V} \\left[ (R+1)c_A \\dot V_0 (1 + \\epsilon_A x_{A0}U_A)\\right]\\\\\n",
    " &= (R+1)\\frac{d }{d (V/V_0)} \\left[c_{A0} \\left(\\frac{1-U_A}{1+\\epsilon_A x_{A0}U_A}\\right) (1 + \\epsilon_A x_{A0}U_A) \\right]\\\\\n",
    " &= (R+1)c_{A0}\\frac{d (1-U_A) }{d \\tau}=-(R+1)c_{A0}\\frac{d U_A }{d \\tau} \\\\\n",
    "\\Rightarrow \\int_0^\\tau \\tau &= \\tau = \\frac{-(R+1)c_{A0}}{\\nu_{A1}} \\int_{U_{A1}}^{U_{A}} \\frac{1}{r_1} d U_A = \\frac{-(R+1)c_{A0}}{\\nu_{A1}} \\int_{U_{A1}}^{U_{A}} \\frac{1}{k_1 c_{A0}\\left(\\frac{1-U_A}{1+\\epsilon_A x_{A0}U_A} \\right)} d U_A \\\\\n",
    "\\frac{(-\\nu_{A1})k \\tau}{R+1} &= \\int_{U_{A1}}^{U_{A}} \\frac{1+\\epsilon_A x_{A0}U_A}{1-U_A} d U_A = \\int_{U_{A1}}^{U_{A}} \\frac{\\epsilon_A x_{A0}}{-1}d U_A + \\int_{U_{A1}}^{U_{A}} \\frac{\\epsilon_A x_{A0}+1}{1-U_A} d U_A\\\\\n",
    " &= -\\epsilon_A x_{A0} U_A \\Big |_{\\frac{R}{R+1}U_A}^{U_A} - (\\epsilon_A x_{A0} +1) \\times ln (1-U_A)\\Big |_{\\frac{R}{R+1}U_A}^{U_A} \\\\\n",
    " &= -\\epsilon_A x_{A0} U_A \\left(1-\\frac{R}{R+1} \\right) + (\\epsilon_A x_{A0} +1) \\times ln \\left(\\frac{1-\\frac{R}{R+1}U_A}{1-U_A} \\right) \\\\\n",
    " \\\\\n",
    "\\bf{\\epsilon_A} &= 0 \\\\\n",
    "\\Rightarrow \\frac{(-\\nu_{A1})k \\tau}{R+1}  &= ln \\left(\\frac{1 - \\frac{R}{R+1}U_A}{1-U_A}\\right)\\\\\n",
    "U_A &= \\frac{1-exp((-\\nu_{A1})k\\tau/(R+1))}{\\frac{R}{R+1}-exp((-\\nu_{A1})k\\tau/(R+1))}\n",
    "\\end{array}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "UA = ['0.993262', '0.886439', '0.863575', '0.833334']\n"
     ]
    }
   ],
   "source": [
    "ua = [(1-np.exp((-1*-1)*5.0/(r+1)))/(r/(r+1)-np.exp((-1*-1)*5.0/(r+1))) for \n",
    "      r in [0., 5., 10., 1e6]]\n",
    "print ('UA = ' + str(list(map(lambda x: '{0:g}'.format(x), ua))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# B 4-5 Fogler \n",
    "\n",
    "Ergun-Gl.\n",
    "\n",
    "$\\frac{dP}{dz}=-\\frac{G}{\\rho g_c D_p}\\cdot\\left(\\frac{1-\\phi}{\\phi^3}\\right)\\left[\\frac{150(1-\\phi)\\mu}{D_p}+1,75G\\right]$\n",
    "\n",
    "Kont.\n",
    "\n",
    "$\\rho v =\\rho_0 v_0$\n",
    "\n",
    "$v = v_0 \\frac{P_0}{P}\\left(\\frac{T}{T_0}\\right)\\frac{F_T}{F_{T0}}$\n",
    "\n",
    "$\\Rightarrow \\frac{dP}{dz}=-\\underbrace{\\frac{G}{\\rho_0 g_c D_p}\\cdot\\left(\\frac{1-\\phi}{\\phi^3}\\right)\\left[\\frac{150(1-\\phi)\\mu}{D_p}+1,75G\\right]}_{\\beta_0}\\frac{P_0}{P}\\left(\\frac{T}{T_0}\\right)\\frac{F_T}{F_{T0}}$\n",
    "\n",
    "$\\begin{array}{ccccc}\n",
    "W &=&(1-\\phi)A_c \\cdot z& \\cdot &\\rho_c\\\\\n",
    "\\text{Masse Kat.} & = & \\text{Kat. Volumen} & \\cdot & \\text{Kat. Feststoffdichte}\n",
    "\\end{array}$\n",
    "\n",
    "$\\Rightarrow \\frac{dP}{dW}=-\\frac{\\beta_0}{A_c(1-\\phi)\\rho_c}\\frac{P_0}{P}\\left(\\frac{T}{T_0}\\right)\\frac{F_T}{F_{T0}}$\n",
    "\n",
    "Um eine Analytische Lösung zu finden trifft man folgende Annahmen:\n",
    "\n",
    "* Einzelne Reaktion: $\\frac{F_T}{F_{T0}}=1+\\epsilon_A X_A$\n",
    "* Isotherm: $T=T_0$\n",
    "* Vernachlässigbare Volumenänderung (oder u. U. Umsatz): $\\epsilon_A X << 1$\n",
    "\n",
    "\n",
    "$\\Rightarrow \\frac{dP}{dW}=-\\frac{\\beta_0}{A_c(1-\\phi)\\rho_c}\\frac{P_0}{P}$\n",
    "\n",
    "$\\frac{P}{P_0} = \\left( 1-\\frac{2 \\beta_0 z}{P_0}\\right)^{1/2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ohne Reaktion: epsilon = 0\n",
      "tr = 4.03902\n",
      "pr = 0.274725\n",
      "rho_0 = 0.4129 lbm/ft^3\n",
      "mu = 0.0671709 lbm/ft/h\n",
      "u = 17884.5 ft/h\n",
      "Ac = 0.0141377 ft^2\n",
      "G = 7384.5 lbm/ft^2/h\n",
      "beta_0 = 163.886 lbf/ft^3\n",
      "beta_0 = 1.13809 psi/ft\n",
      "beta_0 = 0.0775122 atm/ft\n",
      "bei z=L: P/P_0 = 0.264298\n",
      "bei z=L: P = 2.64298atm\n",
      "bei z=L: Delta P = 7.35702atm (Druckverlust)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1645cab2470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "l_r = 60 # ft\n",
    "d = 1.610 * 1/12 # ft <<== (1+1/2)in sched 40\n",
    "dp = 1/4. * 1/12 # ft\n",
    "gc = 32.174 # lbm ft/(s^2 lbf)\n",
    "t = 260 +273.15 # °K\n",
    "phi = 0.45 \n",
    "p0 = 10 # atm\n",
    "mm = (0.78*28.+ 0.21*32. + 0.01*40) # g/mol\n",
    "# Viskosität bei 77°C, 1atm\n",
    "mu = 1.82e-5 * 1000/454 * 30.48/100 * \\\n",
    "        60**2 # kg/m/s * 1000g/kg * 1lbm/454g * \n",
    "# 1m/100cm * 30,48cm/ft * 60^2s/h = lbm/ft/h\n",
    "\n",
    "# Transporteigenschaften, nach äquivalenten Zuständen\n",
    "#\n",
    "# Bird, R. Byron ; Stewart, Warren E. ; Lightfoot, \n",
    "# Edwin N.: Transport Phenomena. New York: \n",
    "# John Wiley & Sons, 2007.\n",
    "tc = 132 # °K --- Luft (Bird S. 879)\n",
    "pc = 36.4 # atm --- Luft (Bird S. 879)\n",
    "vmc = 86.6 # cm^3/mol --- Luft (Bird S. 879)\n",
    "muc = 193.*1e-6 # g/cm/s --- Luft (Bird S. 879)\n",
    "\n",
    "# Transporteigenschaften bei 10 atm, 260°C\n",
    "tr = t/tc\n",
    "pr = p0/pc\n",
    "mur = 1.44 # -- Reduzierte Viskosität (Bird S. 37)\n",
    "mu = mur * muc * 1/454 * 30.48 * 60**2 # g/cm/s * \n",
    "# 1lbm/454g * 30,48cm/ft * 60^2s/h = lbm/ft/h\n",
    "\n",
    "rho0 = p0*101325/(8.314*t) * mm * \\\n",
    "    1/454 * (30.48/100)**3 # Nm/m^3/(Nm/mol/°K*°K) * \n",
    "# g/mol = g/m^3 * 1lbm/454g * \n",
    "# (1m/100cm * 30,48cm/ft)^3 = lbm / ft^3\n",
    "\n",
    "epsilon = 0 # keine Reaktion\n",
    "m_dot = 104.4 # lb/h\n",
    "ac = 1/4. * np.pi * d**2 # ft^2\n",
    "u = m_dot / rho0 / ac # ft/h\n",
    "g = rho0 * u # lbm / ft^2 / h\n",
    "gc = 32.174 * (60**2)**2 # lbm ft /lbf/s^2 * (60^2s/h)\n",
    "beta_0 = g / rho0 / gc / dp * (\n",
    "        (1-phi)/phi**3*(150*(1-phi)*mu/dp+1.75*g)\n",
    "    ) # lbm/ft^2/h * \n",
    "# ft^3/lbm * h^2 lbf/lbm/ft * 1/ft * lbm/ft^2/h \n",
    "# = lbf/ft^2/ft\n",
    "p_d_p_0 = (\n",
    "    1 - 2 * beta_0 * l_r / p0 * 1/101325. * \\\n",
    "    454/1000 * 100/30.48 * 32.174\n",
    ")**(1/2.)\n",
    "# lbf/ft^2/ft * ft / atm * 1atm/101325Pa * \n",
    "# 1Pa/kg*m*s^2 * 1kg/1000g * 454g/lbm *\n",
    "# 100cm/m * 1ft/30,48cm * 32,174 ft lbm/s^2/lbf\n",
    "print('ohne Reaktion: epsilon' + ' = ' + \n",
    "     '{:g}'.format(epsilon))\n",
    "print('tr' + ' = ' + \n",
    "     '{:g}'.format(tr) + '')\n",
    "print('pr' + ' = ' + \n",
    "     '{:g}'.format(pr) + '')\n",
    "print('rho_0' + ' = ' + \n",
    "     '{:g}'.format(rho0) + ' lbm/ft^3')\n",
    "print('mu' + ' = ' + \n",
    "     '{:g}'.format(mu) + ' lbm/ft/h')\n",
    "print('u' + ' = ' + \n",
    "     '{:g}'.format(u) + ' ft/h')\n",
    "print('Ac' + ' = ' + \n",
    "     '{:g}'.format(ac) + ' ft^2')\n",
    "print('G' + ' = ' + \n",
    "     '{:g}'.format(g) + ' lbm/ft^2/h')\n",
    "print('beta_0' + ' = ' + \n",
    "     '{:g}'.format(beta_0) + ' lbf/ft^3')\n",
    "#lbf/ft^2/ft * (1ft/12in)**2 * 1psi/lbf*1in^2 \n",
    "# = psi/ft\n",
    "print('beta_0' + ' = ' + \n",
    "     '{:g}'.format(beta_0 * 1/12**2) + ' psi/ft')\n",
    "# lbf/ft^2/ft * 32,174 ft lbm/s^2/lbf * \n",
    "# (1ft/30,48cm * 100cm/m)^2 * 454g/lbm * 1kg/1000g * \n",
    "# 1Pa / kg*m*s^2 * 1 kPa / 1000 = kPa/m\n",
    "print('beta_0' + ' = ' + \n",
    "     '{:g}'.format(\n",
    "         beta_0 * 32.174 * (\n",
    "             100/30.48) * 454/1000.*1/101325. \n",
    "     ) + ' atm/ft')\n",
    "# kPa/m * 1000Pa/kPa * 1atm/101325Pa * \n",
    "# 1m/100cm*30,48cm/ft = atm/ft\n",
    "print('bei z=L: P/P_0 = ' + \n",
    "     '{:g}'.format(p_d_p_0))\n",
    "print('bei z=L: P = ' + \n",
    "     '{:g}'.format(p_d_p_0 * p0) + 'atm')\n",
    "print('bei z=L: Delta P = ' + \n",
    "     '{:g}'.format(p0 * (1-p_d_p_0)) + \n",
    "      'atm (Druckverlust)')\n",
    "\n",
    "z = np.linspace(0,l_r,50)\n",
    "p = (\n",
    "    1 - 2 * beta_0 * z / p0 * 1/101325. * \\\n",
    "    454/1000 * 100/30.48 * 32.174\n",
    ")**(1/2.) * p0\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "ax.plot(z, p)\n",
    "ax.set_xlabel('z, ft')\n",
    "ax.set_ylabel('p, atm');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# B 4-6 Fogler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reaktion\n",
    "\n",
    "$A+\\frac{1}{2}B \\rightarrow C$\n",
    "\n",
    "Mengenbilanz\n",
    "\n",
    "$F_{A0} \\frac{dX}{dW}=-r_A'$\n",
    "\n",
    "Kinetische Betrachtung\n",
    "$-r_A'=k \\cdot p_A^{1/3}p_B^{2/3}=k \\cdot p_A^{1/3}p_B^{2/3}= k \\cdot R T c_A^{1/3}c_B^{2/3}$ \n",
    "\n",
    "Stöchiometrie, Gasphase und isotherm $v=v_0(1+\\epsilon_A X_A)(P_0/P)$\n",
    "\n",
    "$c_A =\\frac{F_A}{v}= \\frac{c_{A0}(1-X_A)}{1+\\epsilon_A X}\\left(\\frac{P}{P_0}\\right)$\n",
    "\n",
    "$c_B =\\frac{F_A}{v}= \\frac{c_{A0}(c_{B0}/c_{A0}-X_A/2)}{1+\\epsilon_A X}\\left(\\frac{P}{P_0}\\right)$\n",
    "\n",
    "r Als Funktion des Umsatzes\n",
    "\n",
    "$\\begin{array}{cl}\n",
    "-r_A'&=k \\cdot R T_0 \\left[\\frac{c_{A0}(1-X_A)}{1+\\epsilon_A X}\\left(\\frac{P}{P_0}\\right) \\right]^{1/3}\\cdot \\left[\\frac{c_{A0}(c_{B0}/c_{A0}-X_A/2)}{1+\\epsilon_A X}\\left(\\frac{P}{P_0}\\right) \\right]^{2/3}\\\\\n",
    "&=\\frac{k c_{A0}\\cdot R T_0}{1+\\epsilon_A X_A}\\left(\\frac{P}{P_0}\\right)(1-X_A)^{1/3}(c_{B0}/c_{A0}-X_A/2)^{2/3}\n",
    "\\end{array}$\n",
    "\n",
    "Stöchiometrische Einspeisung $c_{B0}/c_{A0}=1/2$, und mit $k\\cdot c_{A0}R T_0 (1/2)^{2/3}=k p_{A0} = k'$\n",
    "\n",
    "$\\Rightarrow -r_A' = k' \\cdot\\left(\\frac{1-X_A}{1+\\epsilon_A X_A}\\right)\\frac{P}{P_0}$\n",
    "\n",
    "PBR Druckverlust bei $\\epsilon_A X_A << 1$:\n",
    "\n",
    "$\\frac{P}{P_0} = \\left( 1-\\frac{2 \\beta_0 z}{P_0}\\right)^{1/2} = \\left( 1-\\underbrace{\\frac{2 \\beta_0}{A_c(1-\\phi)\\rho_c\\cdot P_0}}_{\\alpha}\\cdot W\\right)^{1/2}= (1-\\alpha \\cdot W)^{1/2}$ \n",
    "\n",
    "Auslegungsgleichung\n",
    "\n",
    "$F_{A0} \\frac{dX}{dW}=-r_A'=k' \\cdot\\left(\\frac{1-X_A}{1+\\epsilon_A X_A}\\right)(1-\\alpha \\cdot W)^{1/2}$\n",
    "\n",
    "$\\int\\limits_{0}^{X_A}{\\frac{F_{A0}(1+\\epsilon_A X_A)}{k'(1-X_A)}dX}=\\int\\limits_0^W{(1-\\alpha\\cdot W)^{1/2}dW}$\n",
    "\n",
    "$\\Rightarrow W=\\frac{1-[1-(3\\alpha F_{A0}/2k')\\{(1+\\epsilon_A)ln[1/(1-X_A)]-\\epsilon_A X_A\\}]^{2/3}}{\\alpha}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mit Reaktion: epsilon = -0.15\n",
      "fa0 = 1.08 lbmol/h\n",
      "fb0 = 0.54 lbmol/h\n",
      "fi0 = 2.03143 lbmol/h\n",
      "ft0 = 3.65143 lbmol/h\n",
      "tr = 4.03902\n",
      "pr = 0.274725\n",
      "rho_0 = 0.412875 lbm/ft^3\n",
      "mu = 0.0671709 lbm/ft/h\n",
      "p_{A0} = 3 atm\n",
      "k' = 0.0266473 lbmol/(lbcat h)\n",
      "dot m = 104.4 lbm/h\n",
      "u = 17885.6 ft/h\n",
      "Ac = 0.0141377 ft^2\n",
      "G = 7384.5 lbm/ft^2/h\n",
      "beta_0 = 163.895 lbf/ft^3\n",
      "beta_0 = 1.13816 psi/ft\n",
      "beta_0 = 0.0775169 atm/ft\n",
      "alpha = 0.0166151 lbmKat^-1\n",
      "w = 45.3509 lbmKat\n",
      "L = 48.6029 ft (für die 45.3509lbmKat)\n",
      "bei z=L: P/P_0 = 0.496478\n",
      "bei z=L: P = 4.96478atm\n",
      "bei z=L: Delta P = 5.03522atm (Druckverlust)\n",
      "\n",
      "Ohne Druckverlust-Berücksichtigung:\n",
      "w = 35.2138 lbmKat\n",
      "L = 37.739 ft (für die 35.2138lbmKat)\n",
      "x_A = 0.532108 (zu wenig)\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1645e877048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "x_a = 0.60 # Angabe: Umsatz 60%\n",
    "nt = 10 * 100 # 10 Gruppen mit je 100 Rohren\n",
    "d = 1.610 * 1/12 # ft <<== (1+1/2)in sched 40\n",
    "dp = 1/4. * 1/12 # ft\n",
    "rhoc = 120 # lb/ft^3\n",
    "gc = 32.174 # lbm ft/(s^2 lbf)\n",
    "t = 260 +273.15 # °K\n",
    "phi = 0.45 \n",
    "p0 = 10 # atm\n",
    "mm = (0.78*28.+ 0.21*32. + 0.01*40) # g/mol\n",
    "# c_{B0}/c_{A0}=1/2\n",
    "fa0 = 0.30/nt * 60**2 # lbmol/s * 60^2 s/h = lbmol/h\n",
    "fb0 = 0.30/2/nt * 60**2 # lbmol/s * 60^2 s/h = lbmol/h\n",
    "# Innertstoffe, hauptsächlich N2\n",
    "fi0 = 0.30/2/nt * 60**2 * \\\n",
    "    1/0.21*(1-0.21) # lbmol/s * 60^2 s/h = lbmol/h\n",
    "ft0 = fa0 + fb0 + fi0\n",
    "ya0 = round(fa0/ft0,2)\n",
    "delta = 1-1/2.-1\n",
    "e_a = ya0 * delta\n",
    "pa0 = ya0 * p0\n",
    "k = 0.0141 # lbmol/(atm lbcat h) bei 260°C\n",
    "k_strich = k * pa0 * (\n",
    "    1/2)**(2/3.) # lbmol/(lbcat h) bei 260°C\n",
    "mma = 12*2+4. # lbm/lbmol\n",
    "mmb = 2*16. # lbm/lbmol\n",
    "mmi = 14*2. # lbm/lbmol\n",
    "m_dot = fa0 * mma + fb0 * mmb + fi0 * mmi # lbm/h\n",
    "\n",
    "# Transporteigenschaften, nach äquivalenten Zuständen\n",
    "#\n",
    "# Bird, R. Byron ; Stewart, Warren E. ; Lightfoot, \n",
    "# Edwin N.: Transport Phenomena. New York: \n",
    "# John Wiley & Sons, 2007.\n",
    "tc = 132 # °K --- Luft (Bird S. 879)\n",
    "pc = 36.4 # atm --- Luft (Bird S. 879)\n",
    "vmc = 86.6 # cm^3/mol --- Luft (Bird S. 879)\n",
    "muc = 193.*1e-6 # g/cm/s --- Luft (Bird S. 879)\n",
    "\n",
    "# ========\n",
    "# Transporteigenschaften bei 10 atm, 260°C\n",
    "tr = t/tc\n",
    "pr = p0/pc\n",
    "mur = 1.44 # -- Reduzierte Viskosität (Bird S. 37)\n",
    "mu = mur * muc * 1/454 * 30.48 * 60**2 # g/cm/s * \n",
    "# 1lbm/454g * 30,48cm/ft * 60^2s/h = lbm/ft/h\n",
    "\n",
    "rho0 = p0*101325/(8.3145*t) * mm * \\\n",
    "    1/454 * (30.48/100)**3 # Nm/m^3/(Nm/mol/°K*°K) * \n",
    "# g/mol = g/m^3 * 1lbm/454g * \n",
    "# (1m/100cm * 30,48cm/ft)^3 = lbm / ft^3\n",
    "\n",
    "# ========\n",
    "\n",
    "ac = np.pi / 4 * d**2 # ft^2 \n",
    "u = m_dot / rho0 / ac # ft / h\n",
    "g = rho0 * u # lbm/ft^2/h\n",
    "gc = 32.174 * (60**2)**2 # lbm ft /lbf/s^2 * (60^2s/h)\n",
    "beta_0 = g / rho0 / gc / dp * (\n",
    "        (1-phi)/phi**3*(150*(1-phi)*mu/dp+1.75*g)\n",
    "    ) # lbm/ft^2/h * \n",
    "# ft^3/lbm * h^2 lbf/lbm/ft * 1/ft * lbm/ft^2/h \n",
    "# = lbf/ft^2/ft\n",
    "alpha = 2 * beta_0 / (\n",
    "    ac * (1-phi) * rhoc * p0\n",
    ") * 1/101325./1000.*454.*100./30.48*32.174\n",
    "# lbf/ft^3 * 1/ft^2 * ft^3/lbmKat * 1/atm * \n",
    "# 1atm/101325Pa * 1Pa/kgKat*m*s^2 * 1kgKat/1000gKat * \n",
    "# 454gKat/1lbmKat * 100cm/1m * 1ft/30,48cm * \n",
    "# 32,174 ft lbmKat/s^2/lbf = lbmKat^-1\n",
    "w = (1-(1-(3/2.*alpha*fa0/k_strich) * (\n",
    "    (1+e_a) * np.log(\n",
    "        1/(1-x_a)\n",
    "    ) - e_a * x_a\n",
    "))**(2/3.))/alpha # lbmKat\n",
    "l_r = w/((1-phi)*ac*rhoc) # ft\n",
    "p_d_p_0 = (\n",
    "    1 - 2 * beta_0 * l_r / p0 * 1/101325. * \\\n",
    "    454/1000 * 100/30.48 * 32.174\n",
    ")**(1/2.)\n",
    "# lbf/ft^2/ft * ft / atm * 1atm/101325Pa * \n",
    "# 1Pa/kg*m*s^2 * 1kg/1000g * 454g/lbm *\n",
    "# 100cm/m * 1ft/30,48cm * 32,174 ft lbm/s^2/lbf\n",
    "print('Mit Reaktion: epsilon' + ' = ' + \n",
    "     '{:g}'.format(e_a))\n",
    "for item in ['fa0', 'fb0', 'fi0', 'ft0']:\n",
    "    print(item + ' = ' + \n",
    "     '{:g}'.format(locals()[item]) + ' lbmol/h')\n",
    "print('tr' + ' = ' + \n",
    "     '{:g}'.format(tr) + '')\n",
    "print('pr' + ' = ' + \n",
    "     '{:g}'.format(pr) + '')\n",
    "print('rho_0' + ' = ' + \n",
    "     '{:g}'.format(rho0) + ' lbm/ft^3')\n",
    "print('mu' + ' = ' + \n",
    "     '{:g}'.format(mu) + ' lbm/ft/h')\n",
    "print('p_{A0}' + ' = ' + \n",
    "     '{:g}'.format(pa0) + ' atm')\n",
    "print('k' + \"'\" + ' = ' + \n",
    "     '{:g}'.format(k_strich) + ' lbmol/(lbcat h)')\n",
    "print('dot m' + ' = ' + \n",
    "     '{:g}'.format(m_dot) + ' lbm/h')\n",
    "print('u' + ' = ' + \n",
    "     '{:g}'.format(u) + ' ft/h')\n",
    "print('Ac' + ' = ' + \n",
    "     '{:g}'.format(ac) + ' ft^2')\n",
    "print('G' + ' = ' + \n",
    "     '{:g}'.format(g) + ' lbm/ft^2/h')\n",
    "print('beta_0' + ' = ' + \n",
    "     '{:g}'.format(beta_0) + ' lbf/ft^3')\n",
    "#lbf/ft^2/ft * (1ft/12in)**2 * 1psi/lbf*1in^2 \n",
    "# = psi/ft\n",
    "print('beta_0' + ' = ' + \n",
    "     '{:g}'.format(beta_0 * 1/12**2) + ' psi/ft')\n",
    "# lbf/ft^2/ft * 32,174 ft lbm/s^2/lbf * \n",
    "# (1ft/30,48cm * 100cm/m)^2 * 454g/lbm * 1kg/1000g * \n",
    "# 1Pa / kg*m*s^2 * 1 kPa / 1000 = kPa/m\n",
    "print('beta_0' + ' = ' + \n",
    "     '{:g}'.format(\n",
    "         beta_0 * 32.174 * (\n",
    "             100/30.48) * 454/1000.*1/101325. \n",
    "     ) + ' atm/ft')\n",
    "# kPa/m * 1000Pa/kPa * 1atm/101325Pa * \n",
    "# 1m/100cm*30,48cm/ft = atm/ft\n",
    "print('alpha' + ' = ' + \n",
    "     '{:g}'.format(alpha) + ' lbmKat^-1')\n",
    "print('w' + ' = ' + \n",
    "     '{:g}'.format(w) + ' lbmKat')\n",
    "print('L' + ' = ' + \n",
    "     '{:g}'.format(l_r) + ' ft (für die ' + \n",
    "      '{:g}'.format(w) + 'lbmKat)')\n",
    "print('bei z=L: P/P_0 = ' + \n",
    "     '{:g}'.format(p_d_p_0))\n",
    "print('bei z=L: P = ' + \n",
    "     '{:g}'.format(p_d_p_0 * p0) + 'atm')\n",
    "print('bei z=L: Delta P = ' + \n",
    "     '{:g}'.format(p0 * (1-p_d_p_0)) + \n",
    "      'atm (Druckverlust)')\n",
    "\n",
    "def x_a_func(w, x_a_0):\n",
    "    # a*ln(1/(1-x))-b x == c \n",
    "    # einfach iterativ nach x lösen\n",
    "    x_a = x_a_0\n",
    "    for i in range(10):\n",
    "        x_a = 1-np.exp(\n",
    "            -(k_strich/fa0 * (\n",
    "                2/3./alpha*(1-(1-alpha*w)**(3/2))\n",
    "            ) +e_a*x_a)/(e_a+1)\n",
    "        )\n",
    "    return x_a\n",
    "\n",
    "z = np.linspace(0,l_r,50)\n",
    "p = (1 - alpha * z*(1-phi)*ac*rhoc)**(1/2.) * p0\n",
    "x_a_reihe = np.array([\n",
    "    x_a_func(w, x_a) \n",
    "    for w in z * (1-phi) * ac * rhoc\n",
    "]) \n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(2,1,1)\n",
    "ax.plot(z, p)\n",
    "ax.set_xlabel('z, ft')\n",
    "ax.set_ylabel('p, atm');\n",
    "\n",
    "ax = fig.add_subplot(2,1,2)\n",
    "ax.plot(z, x_a_reihe)\n",
    "ax.set_xlabel('z, ft')\n",
    "ax.set_ylabel('$x_A$');\n",
    "\n",
    "print('')\n",
    "print('Ohne Druckverlust-Berücksichtigung:')\n",
    "w = fa0/k_strich * (\n",
    "    (1+e_a)*np.log(1/(1-x_a))-e_a*x_a) # lbmKat\n",
    "l_r = w/((1-phi)*ac*rhoc) # ft\n",
    "print('w' + ' = ' + \n",
    "     '{:g}'.format(w) + ' lbmKat')\n",
    "print('L' + ' = ' + \n",
    "     '{:g}'.format(l_r) + ' ft (für die ' + \n",
    "      '{:g}'.format(w) + 'lbmKat)')\n",
    "print('x_A' + ' = ' + \n",
    "     '{:g}'.format(x_a_func(w, x_a)) + \n",
    "      ' (zu wenig)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# B 4-7 Fogler\n",
    "Eine Annahme weniger:\n",
    "* Einzelne Reaktion: $\\frac{F_T}{F_{T0}}=1+\\epsilon_A X_A$\n",
    "* Isotherm: $T=T_0$\n",
    "\n",
    "(Volumenänderung berücksichtigt): $\\epsilon_A X_A$\n",
    "\n",
    "Ergun-Gleichung reduziert zu:\n",
    "\n",
    "$\\Rightarrow \n",
    "\\begin{array}{cl} \n",
    "\\frac{dP}{dW}&=-\\frac{\\beta_0}{A_c(1-\\phi)\\rho_c}\\frac{P_0}{P}\\left(\\frac{T}{T_0}\\right)\\frac{F_T}{F_{T0}}\\\\\n",
    "&= -\\frac{\\alpha}{2}\\frac{P_0}{P/P_0}\\cdot(1+\\epsilon_A X_A)\n",
    "\\end{array}$\n",
    "\n",
    "Zu lösendes System:\n",
    "\n",
    "$\\begin{array}{cl} \n",
    "\\frac{dP/P_0}{dW}&= -\\frac{\\alpha}{2}\\frac{1+\\epsilon_A X_A}{P/P_0}\\\\\n",
    "\\frac{dX_A}{dW}&=\\frac{k'}{F_{A0}} \\cdot\\left(\\frac{1-X_A}{1+\\epsilon_A X_A}\\right)\\frac{P}{P_0}\n",
    "\\end{array}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1645d21e048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1645ea75cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy import integrate\n",
    "from scipy.interpolate import interp1d\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.ticker import MultipleLocator, FormatStrFormatter\n",
    "%matplotlib inline\n",
    "x_a = 0.60 # Angabe: Umsatz 60%\n",
    "nt = 10 * 100 # 10 Gruppen mit je 100 Rohren\n",
    "d = 1.610 * 1/12 # ft <<== (1+1/2)in sched 40\n",
    "dp = 1/4. * 1/12 # ft\n",
    "rhoc = 120 # lb/ft^3\n",
    "gc = 32.174 # lbm ft/(s^2 lbf)\n",
    "t = 260 +273.15 # °K\n",
    "phi = 0.45 \n",
    "p0 = 10 # atm\n",
    "mm = (0.78*28.+ 0.21*32. + 0.01*40) # g/mol\n",
    "# c_{B0}/c_{A0}=1/2\n",
    "fa0 = 0.30/nt * 60**2 # lbmol/s * 60^2 s/h = lbmol/h\n",
    "fb0 = 0.30/2/nt * 60**2 # lbmol/s * 60^2 s/h = lbmol/h\n",
    "# Innertstoffe, hauptsächlich N2\n",
    "fi0 = 0.30/2/nt * 60**2 * \\\n",
    "    1/0.21*(1-0.21) # lbmol/s * 60^2 s/h = lbmol/h\n",
    "ft0 = fa0 + fb0 + fi0\n",
    "ya0 = round(fa0/ft0, 2)\n",
    "delta = 1-1/2.-1\n",
    "e_a = ya0 * delta\n",
    "pa0 = ya0 * p0\n",
    "k = 0.0141 # lbmol/(atm lbcat h) bei 260°C\n",
    "k_strich = k * pa0 * (\n",
    "    1/2)**(2/3) # lbmol/(lbcat h) bei 260°C\n",
    "mma = 12*2+4. # lbm/lbmol\n",
    "mmb = 2*16. # lbm/lbmol\n",
    "mmi = 14*2. # lbm/lbmol\n",
    "m_dot = fa0 * mma + fb0 * mmb + fi0 * mmi # lbm/h\n",
    "\n",
    "# Transporteigenschaften, nach äquivalenten Zuständen\n",
    "#\n",
    "# Bird, R. Byron ; Stewart, Warren E. ; Lightfoot, \n",
    "# Edwin N.: Transport Phenomena. New York: \n",
    "# John Wiley & Sons, 2007.\n",
    "tc = 132 # °K --- Luft (Bird S. 879)\n",
    "pc = 36.4 # atm --- Luft (Bird S. 879)\n",
    "vmc = 86.6 # cm^3/mol --- Luft (Bird S. 879)\n",
    "muc = 193.*1e-6 # g/cm/s --- Luft (Bird S. 879)\n",
    "\n",
    "# ========\n",
    "# Transporteigenschaften bei 10 atm, 260°C\n",
    "tr = t/tc\n",
    "pr = p0/pc\n",
    "mur = 1.44 # -- Reduzierte Viskosität (Bird S. 37)\n",
    "mu = mur * muc * 1/454 * 30.48 * 60**2 # g/cm/s * \n",
    "# 1lbm/454g * 30,48cm/ft * 60^2s/h = lbm/ft/h\n",
    "\n",
    "rho0 = p0*101325/(8.3145*t) * mm * \\\n",
    "    1/454 * (30.48/100)**3 # Nm/m^3/(Nm/mol/°K*°K) * \n",
    "# g/mol = g/m^3 * 1lbm/454g * \n",
    "# (1m/100cm * 30,48cm/ft)^3 = lbm / ft^3\n",
    "\n",
    "# ========\n",
    "\n",
    "ac = np.pi / 4 * d**2 # ft^2 \n",
    "u = m_dot / rho0 / ac # ft / h\n",
    "g = rho0 * u # lbm/ft^2/h\n",
    "gc = 32.174 * (60**2)**2 # lbm ft /lbf/s^2 * (60^2s/h)\n",
    "beta_0 = g / rho0 / gc / dp * (\n",
    "        (1-phi)/phi**3*(150*(1-phi)*mu/dp+1.75*g)\n",
    "    ) # lbm/ft^2/h * \n",
    "# ft^3/lbm * h^2 lbf/lbm/ft * 1/ft * lbm/ft^2/h \n",
    "# = lbf/ft^2/ft\n",
    "alpha = 2 * beta_0 / (\n",
    "    ac * (1-phi) * rhoc * p0\n",
    ") * 1/101325./1000.*454.*100./30.48*32.174\n",
    "# lbf/ft^3 * 1/ft^2 * ft^3/lbmKat * 1/atm * \n",
    "# 1atm/101325Pa * 1Pa/kgKat*m*s^2 * 1kgKat/1000gKat * \n",
    "# 454gKat/1lbmKat * 100cm/1m * 1ft/30,48cm * \n",
    "# 32,174 ft lbmKat/s^2/lbf = lbmKat^-1\n",
    "\n",
    "# Katalysatorgewicht ohne Berücksichtigung von \n",
    "# e_a x_a im Druckverlust\n",
    "w = (1-(1-(3/2.*alpha*fa0/k_strich) * (\n",
    "    (1+e_a) * np.log(\n",
    "        1/(1-x_a)\n",
    "    ) - e_a * x_a\n",
    "))**(2/3.))/alpha # lbmKat\n",
    "l_r = w/((1-phi)*ac*rhoc) # ft\n",
    "p_d_p_0 = (\n",
    "    1 - 2 * beta_0 * l_r / p0 * 1/101325. * \\\n",
    "    454/1000 * 100/30.48 * 32.174\n",
    ")**(1/2.)\n",
    "# Funktion für den Fall ohne Berücksichtigung von \n",
    "# e_a x_a im Druckverlust\n",
    "def x_a_func_ohne(w, x_a_0):\n",
    "    # a*ln(1/(1-x))-b x == c \n",
    "    # einfach iterativ nach x lösen\n",
    "    x_a = x_a_0\n",
    "    for i in range(10):\n",
    "        x_a = 1-np.exp(\n",
    "            -(k_strich/fa0 * (\n",
    "                2/3./alpha*(1-(1-alpha*w)**(3/2))\n",
    "            ) +e_a*x_a)/(e_a+1)\n",
    "        )\n",
    "    return x_a\n",
    "\n",
    "# Funktion für den Fall mit Berücksichtigung von \n",
    "# e_a x_a im Druckverlust\n",
    "def dydw(y, t0):\n",
    "    p_d_p0 = y[0]\n",
    "    x_a = y[1]\n",
    "    dp_d_p0_dw = -alpha/2. * (1+e_a*x_a)/(p_d_p0)\n",
    "    dx_a_dw = k_strich/fa0*(\n",
    "        (1-x_a)/(1+e_a*x_a)\n",
    "    )*p_d_p0\n",
    "    return np.array([dp_d_p0_dw, dx_a_dw])\n",
    "\n",
    "l_r = 60./((1-phi) * ac * rhoc ) # ft\n",
    "z = np.linspace(0,l_r,50) # ft\n",
    "w = z * (1-phi) * ac * rhoc # lbmKat\n",
    "\n",
    "y, info = integrate.odeint(\n",
    "    dydw, np.array([1.0,0.0]), w, \n",
    "    full_output=True)\n",
    "\n",
    "p_d_p0 = y[:,0]\n",
    "x_a = y[:,1]\n",
    "\n",
    "p_d_p0_ohne = (\n",
    "    1-2*beta_0*z/p0*1/101325./1000.*454.*100./30.48*32.174\n",
    ")**(1/2.)\n",
    "p_d_p0_ohne = (\n",
    "    1-alpha*w)**(1/2.)\n",
    "x_a_ohne = x_a_func_ohne(w, 0.6)\n",
    "\n",
    "r_a_strich = -k_strich * (1-x_a)/(1+e_a*x_a) * p_d_p0\n",
    "r_a_strich_ohne = -k_strich * (1-x_a_ohne)/(1+e_a*x_a_ohne) * (1-alpha*w)**(1/2.)\n",
    "\n",
    "\n",
    "majorLocator = MultipleLocator(0.6)\n",
    "majorFormatter = FormatStrFormatter('%0g')\n",
    "minorLocator = MultipleLocator(0.3)\n",
    "majorLocator_x = MultipleLocator(12)\n",
    "majorFormatter_x = FormatStrFormatter('%0g')\n",
    "minorLocator_x = MultipleLocator(6)\n",
    "fig = plt.figure(figsize=(20*12/30.48, 30*12/30.48))\n",
    "ax1 = fig.add_subplot(4,1,1)\n",
    "ax1.plot(w, -r_a_strich*100,\n",
    "         label='mit $\\epsilon_A X_A$ in $P/P_0$')\n",
    "ax1.plot(w, -r_a_strich_ohne*100, '--', \n",
    "         label='ohne $\\epsilon_A X_A$ in $P/P_0$')\n",
    "ax1.set_ylim([0,3])\n",
    "ax1.set_ylabel('$-r_A' + \"'\" + ' \\cdot 10^2$')\n",
    "ax1.legend()\n",
    "plt.setp(ax1.get_xticklabels(), visible=False)\n",
    "ax1.yaxis.set_major_formatter(majorFormatter)\n",
    "ax1.yaxis.set_major_locator(majorLocator)\n",
    "ax1.yaxis.set_minor_locator(minorLocator)\n",
    "\n",
    "ax2 = fig.add_subplot(4,1,2, sharex=ax1)\n",
    "ax2.plot(w, p_d_p0, \n",
    "         label='mit $\\epsilon_A X_A$ in $P/P_0$')\n",
    "ax2.plot(w, p_d_p0_ohne, '--',\n",
    "         label='ohne $\\epsilon_A X_A$ in $P/P_0$')\n",
    "ax2.set_ylabel('p/p0')\n",
    "ax2.legend()\n",
    "plt.setp(ax2.get_xticklabels(), visible=False)\n",
    "\n",
    "ax3 = fig.add_subplot(4,1,3, sharex=ax1)\n",
    "ax3.plot(w, x_a, \n",
    "         label='mit $\\epsilon_A X_A$ in $P/P_0$')\n",
    "ax3.plot(w, x_a_ohne, '--',\n",
    "         label='ohne $\\epsilon_A X_A$ in $P/P_0$')\n",
    "ax3.set_xlabel('w, lbmKat')\n",
    "ax3.set_ylabel('$x_A$')\n",
    "ax3.set_ylim([0,1.0])\n",
    "plt.setp(ax3.get_xticklabels(), visible=False)\n",
    "ax3.axhline(0.6, linestyle=':')\n",
    "ax3.legend()\n",
    "\n",
    "ax4 = fig.add_subplot(4,1,4, sharex=ax1)\n",
    "ax4.plot(w, (1+e_a*x_a)/p_d_p0)\n",
    "ax4.set_xlabel('w, lbmKat')\n",
    "ax4.set_ylabel('$f=v/v_0$')\n",
    "ax4.set_ylim([0,4.0])\n",
    "ax3.set_xlim([0,60])\n",
    "ax4.xaxis.set_major_formatter(majorFormatter_x)\n",
    "ax4.xaxis.set_major_locator(majorLocator_x)\n",
    "ax4.xaxis.set_minor_locator(minorLocator_x);\n",
    "\n",
    "fig2 = plt.figure()\n",
    "ax3 = fig2.add_subplot(111)\n",
    "ax3.plot(w, x_a, \n",
    "         label='mit $\\epsilon_A X_A$ in $P/P_0$')\n",
    "ax3.plot(w, x_a_ohne, '--',\n",
    "         label='ohne $\\epsilon_A X_A$ in $P/P_0$')\n",
    "ax3.set_xlabel('w, lbmKat')\n",
    "ax3.set_ylabel('$x_A$')\n",
    "ax3.set_xlim([0,60])\n",
    "ax3.set_ylim([0,1.0])\n",
    "ax3.axhline(0.6, linestyle=':', color='red')\n",
    "w_fuer_xa_60 = interp1d(x_a, w)(0.6).item()\n",
    "w_fuer_xa_60_ohne = interp1d(x_a_ohne, w)(0.6).item()\n",
    "ax3.annotate(\n",
    "    'mit: ' + '{:0g}'.format(w_fuer_xa_60) + \n",
    "    'lbmKat', \n",
    "    xy=[w_fuer_xa_60, 0.6], \n",
    "    xytext=[-120,-20],\n",
    "    textcoords='offset points',\n",
    "    arrowprops=dict(arrowstyle='->',\n",
    "                    connectionstyle='arc3, rad=0.2'\n",
    "                   )\n",
    ")\n",
    "ax3.annotate(\n",
    "    'ohne: ' + '{:0g}'.format(w_fuer_xa_60_ohne) +\n",
    "    'lbmKat', \n",
    "    xy=[w_fuer_xa_60_ohne, 0.6], \n",
    "    xytext=[+50,-10],\n",
    "    textcoords='offset points',\n",
    "    arrowprops=dict(arrowstyle='->',\n",
    "                    connectionstyle='arc3, rad=0.2'\n",
    "                   )\n",
    ")\n",
    "ax3.legend()\n",
    "ax3.xaxis.set_major_formatter(majorFormatter_x)\n",
    "ax3.xaxis.set_major_locator(majorLocator_x)\n",
    "ax3.xaxis.set_minor_locator(minorLocator_x);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ü 9.8 [5]\n",
    "Irreversible Gasphasenreaktion $A+B\\rightarrow C+D$\n",
    "\n",
    "Für jeden Katalysator hat der Geschwindigkeitsausdruck eine andere Form:\n",
    "\n",
    "$\\begin{array}{cl}\n",
    "r_1 &= \\frac{k c_A c_B}{1+K_A c_A}\\\\\n",
    "r_2 &= \\frac{k c_A c_B}{1+K_A c_A + K_C c_c}\\\\\n",
    "r_3 &= \\frac{k c_A c_B}{(1+K_A c_A + K_B c_B)^2}\\\\\n",
    "r_4 &= \\frac{k c_A c_B}{(1+K_A c_A + K_B c_B + K_C c_C)^2}\\\\\n",
    "\\end{array}$\n",
    "\n",
    "Der Zulaufstrom von A beträgt 1,5mol/min, die Ausgangskonzentrationen der Reaktanden sind $c_{A,0}=c_{B,0}=1mol/L$. Es wird in jedem Fall eine Katalysatormasse von 2 kg benutzt. Es sind gegeben:\n",
    "\n",
    "$\\begin{array}{cl}\n",
    "k &= 10 L^2 kg^{-1}min^{-1}\\\\\n",
    "K_A &= 1 L/mol\\\\\n",
    "K_B &= 2 L/mol\\\\\n",
    "K_C &= 20 L/mol\n",
    "\\end{array}$\n",
    "\n",
    "a) Stellen Sie den Umsatz als Funktion der Katalysatormasse für jeden der Katalysatoren bei konstantem Druck dar.\n",
    "\n",
    "b) Berechne den Einfluss des Druckverlustes auf den Umsatz in den Reaktoren, wenn die folgende Beziehung gegeben ist:\n",
    "\n",
    "$\\frac{dy}{dm}=-\\frac{\\alpha}{2y}$ mit $y=P/P_0$ und $\\alpha=konstant=0,4$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lösung:\n",
    "\n",
    "Mengenbilanz\n",
    "\n",
    "$\\begin{array}{lrl}\n",
    "&\\frac{d \\dot n_{A}}{dm} &=-\\dot n_{A,0}\\frac{d U_A}{dm}=\\nu_{A,1} \\cdot r_1' = r_A'\\\\\n",
    "\\Rightarrow & \\dot n_{A0}\\frac{d U_A}{dm} &= -r_A'\n",
    "\\end{array}$\n",
    "\n",
    "Kinetische Betrachtung\n",
    "\n",
    "$-r_A'= \\nu_{A,1} r_1 = \\frac{k c_A c_B}{1+K_A c_A}$ \n",
    "\n",
    "Stöchiometrie, Gasphase $\\dot V=\\dot V_0(1+\\epsilon_A U_A)(P_0/P)(T/T_0)$\n",
    "\n",
    "$c_A =\\frac{\\dot n_A}{\\dot V}= \\frac{c_{A0}(1-U_A)}{1+\\epsilon_A U_A}\\left(\\frac{P}{P_0}\\right)\\frac{T_0}{T}$\n",
    "\n",
    "$c_B =\\frac{\\dot n_B}{\\dot V}= \\frac{c_{A0}(c_{B0}/c_{A0}-U_A)}{1+\\epsilon_A U_A}\\left(\\frac{P}{P_0}\\right)\\frac{T_0}{T}$\n",
    "\n",
    "Vorgabe: $c_{B0}/c_{A0}=1 \\Rightarrow c_A = c_B$\n",
    "\n",
    "Vorgabe: $T/T_0 =1$\n",
    "\n",
    "r Als Funktion des Umsatzes\n",
    "\n",
    "$\\begin{array}{cl}\n",
    "-r_A'&=\\frac{k \\left[\\frac{c_{A0}(1-U_A)}{1+\\epsilon_A U_A}\\left(\\frac{P}{P_0}\\right)\\frac{T_0}{T} \\right]^2}{1+K_A  \\left[\\frac{c_{A0}(1-U_A)}{1+\\epsilon_A U_A}\\left(\\frac{P}{P_0}\\right)\\frac{T_0}{T} \\right]}\\\\\n",
    "\\end{array}$\n",
    "\n",
    "Auslegungsgleichung\n",
    "\n",
    "$\\dot n_{A0} \\frac{dU_A}{dm}=-r_A'=\\frac{k \\left[\\frac{c_{A0}(1-U_A)}{1+\\epsilon_A U_A}\\left(\\frac{P}{P_0}\\right) \\right]^2}{1+K_A  \\left[\\frac{c_{A0}(1-U_A)}{1+\\epsilon_A U_A}\\left(\\frac{P}{P_0}\\right) \\right]}$\n",
    "\n",
    "PBR Druckverlust nach Ergun-Gleichung reduziert zu:\n",
    "\n",
    "$\\Rightarrow \n",
    "\\begin{array}{cl} \n",
    "\\frac{dP}{dm}&=-\\frac{\\beta_0}{A_c(1-\\phi)\\rho_c}\\frac{P_0}{P}\\left(\\frac{T}{T_0}\\right)\\frac{F_T}{F_{T0}}\\\\\n",
    "&= -\\frac{\\alpha}{2}\\frac{P_0}{P/P_0}\\cdot(1+\\epsilon_A X_A)\n",
    "\\end{array}$\n",
    "\n",
    "Zu lösendes System:\n",
    "\n",
    "$\\begin{array}{cl} \n",
    "\\frac{dP/P_0}{dm}&= -\\frac{\\alpha}{2}\\frac{1+\\epsilon_A X_A}{P/P_0}\\\\\n",
    "\\frac{dU_A}{dm}&=\\frac{\\frac{k}{\\dot n_{A0}} \\left[\\frac{c_{A0}(1-U_A)}{1+\\epsilon_A U_A}\\left(\\frac{P}{P_0}\\right) \\right]^2}{1+K_A  \\left[\\frac{c_{A0}(1-U_A)}{1+\\epsilon_A U_A}\\left(\\frac{P}{P_0}\\right) \\right]}\n",
    "\\end{array}$\n",
    "\n",
    "Randbedingungen: $m=0\\Rightarrow U_A=0, P/P_0=1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1645ea8b898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1645d20cbe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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k41Ii+dm8QRw6foYVuwpYvuurg8bdQgKYNjCWmYPseQU9uuoQ1Up1Rhr+PqxXZFdundSHWyf1obS8is/3FLE88ygrswr4YFse/n7CmN4RzBocy6zBcaTGhHm7ZKWUh2j4K8AeNJ47NJ65Q+OpqTFsyz3J8swCPsk8yh8X7+KPi3eRGh3KTOeLYEzvCJ2rQKkOTMNf/Qc/lyGq750zkNwTtnnok8wCnv9iP099nkOProHMGGi/CKYO0N5Dyjf99Kc/JS4ujnvvvRcAYwwRERHk5eXRtWv7Pvtew181KSmiK9+c2IdvTuxDSXkVn+22s5et3FXAu1sOE+gvTEiN4tIhccwcHKeT1iifsX37dmbPnn3udk5ODjExMe0++EHDXzVTWHDAubkKqmsMmw6c4JPMo3y88yi/en8Hv3p/B0MTuzFrcByzh8QxpGc3RPTkMtU5ZWRkMHz48HO309PTz7vdnmn4qwvm7yfneg/dN38wewtL+Hin/SJ4ePke/vHJHhJ7dGH2EPtFMC4lUruRKs9b8jM4kuHZ54wfBvMebHSVEydOUFFRQXx8/Ln7NPyVT+obE0bfaWHcNa0vRSXlrMgs4KOdR3l1vZ2noFtIAJcMiuXStHimDYghNFg/fqrjqrvXDzb8XYdnvv766xk3bhw/+clP2rq8Jun/PtUqosOCz01wf6bCdiP9eOdRlmce5b2teQQF+DG5X/S54wQx4cHeLll1VE3sobeWrKws+vbte+52TU0Na9as4fHHHwfg/fffZ8GCBXzyySdeqa8pGv6q1XUNCmBOWjxz0uKpqq5h44ETLNtxhI93HmXFrgJEMhiTHHFuneSo9n+wTKnevXvz2GOPUVZWRkhICH/84x+ZOnUq0dHRlJWV8eabb/Lyyy/z9ttve7vUemn4qzYV4G+nqJyQGsWvFwwhM7+Yj3Ye4aMdR/nD4kz+sDiTQfHhXJoWz5w0PWCs2q9LL72UZcuWMWjQIIKDg5kwYcK5vf6HHnqIkpIS7rrrLnbs2MHZs2fp0qV99YLTmbxUu3Ho+BmW7bBfBBsOHMcY6BXZhTlD4pkzNJ7RyRH467DUivY9k9fBgwd54IEHeOaZZwB44IEHmDt3LuPHj2/2c+k0jsrnFJWU88nOoyzbcYQ12ceoqK4hOiyYS9PimJsWz8S+UdpzyIe15/D3JK9P4ygic4GHAX/gaWPMg3WWJwMvAD2cdX5mjFnc0uKU74oOC+aGccncMC6Z4rJKVmYVsmz7Ed7bcphX1h2kW0gAswbHMWeo7Tmkk9or1TxNhr+I+AOPArOBXGCDiCw0xux0We2XwBvGmMdEZAiwGOjTCvUqHxQeEsgVIxK4YkQCZZXVrN5TxFLngPE7Ww7TNcifGQNjmTM0nksGxRKmXUiVapI7/0vGAdnGmH0AIvIacCXgGv4G6OZc7w7kebJIpWqFBPoza0gcs4bEUVldw7p9x1m6I59lO46yKCOfoAA/pvaPZu7QnsweHEf3rjrmkFL1cSf8E4FDLrdzgbpHLu4HPhKR7wOhwKz6nkhE7gTuBEhOTm5urUqdJ9Dfj8n9o5ncP5oHrhjK5oMnWJyRz7LtR/gks4AAP+HiftHMG2qnuIwM1bkJOhNjTKfuCdbax2ObPOArIl8D5hhj7nBufwMYZ4z5vss6P3ae639FZCLwDDDUGFPT0PPqAV/VWowxbMs9xZLt+SzJOMLB42fw9xMmpkYxb5g9lyA6TE8q68hycnIIDw8nKiqqU34BGGM4duwYxcXFpKSknLeszXr7OGF+vzFmjnP7505xf3JZZwcw1xhzyLm9D5hgjClo6Hk1/FVbMMawI+80S7bnszjjCDlFpfgJjE+JYv7wnsxNi9ezizugyspKcnNzKSsr83YprSYkJISkpCQCA89vumzL8A8AdgMzgcPABuAmY8wOl3WWAK8bY54XkcHAciDRNPLkGv6qrRlj2HWkmCUZ+SzKyGdvYSkiMD4lksuG9WTO0Hhiw0O8XaZSjWrTfv4iMh/4B7Yb57PGmD+IyG+BjcaYhU4Pn6eAMOzB3/8xxnzU2HNq+CtvMsaw+2gJizLyWZyRT3ZBCSIwrk8kC0Yk6C8C1W7pSV5KedDuo8UsSs/nw/Q89hbapqEJqVFc5jQNRekxAtVOaPgr1QpqfxF8mJ7HovR89hWVnjtYvGB4T+YOjadHV+01pLxHw1+pVmaMITO/mEUZeXyYns+BY2cI8BOm9I9mwfAEZqfF0U3nLlZtTMNfqTZkjGH74dN8mG6/CA6fPEtQgB/TB8Rw+YgEZg6OpWuQnlmsWp+Gv1JeYoxhy6GTfLDNNg0VFJfTxTnz+IoRCUwdEE1wgI41pFqHhr9S7UB1jWF9znE+TM9jcUY+J85U0i0kgLlD47liRCIT+0bpMNTKozT8lWpnKqtrWJ1dxAfb8vhox1FKyquIDgtmwfCeXDEygVG9enTKs1FV29LwV6odK6usZuWuAhZuy2P5rgIqqmpIjuzKFSMSuHJkAv3jwr1douqgNPyV6iBOl1Xy0Y6jvL/1MGuyi6gxMLhnN64caYepTujRvqb3U+2bhr9SHVBhcTmL0vN4b2seWw+dPHdW8VWjEpk/tKcOQa2apOGvVAe3v6iU97fm8f7Ww+wrKiXI348Zg2K4elQiMwbFao8hVS8Nf6U6idpzCN7dcpiF2/IoKimnW0gAlw3vyVUjE7moTyR+2mNIOTT8leqEqpweQ+9vzWPp9iOcrawmsUcXrh6VyNWjE+kbE+btEpWXafgr1cmVllfx0c4jvLP5qwPFI5K6c83oJC4fkaAzk/koDX+lfEjB6TIWbsvj7c2Hycw/TYCfMGNQLNeO1uMDvkbDXykflZlvjw+8u+UwhcXldO8SyOUjenLt6CRG6olknZ6Gv1I+rqq6hjV7j/H2plyW7ThCeVUNqTGhXDcmiWtGJRHfXWcl64w0/JVS55wuq2RJRj5vbcplw/4TiMDkftFcNyaJOWnxhARqs1BnoeGvlKrX/qJS3tmcy9ubD3P45FnCQwK4fEQC141J0vGFOgENf6VUo2pqDGtzjvHWxlwWb8+nrLKGfrFhtllodKJOVt9BafgrpdxWXFbJovR83tyUy6YDJ/D3E2YMjOFrY3txyaBYAv39vF2icpOGv1LqguwtLOHNjbm8vTmXwuJyosOCuGZ0El8fm0S/WB1ttL3T8FdKtUhVdQ2rsgp5Y+MhVuwqoKrGMDq5BzdclMxlw3sSGqzTUrZHGv5KKY8pLC7n3S25vLExl+yCEkKD/Ll8RAI3jEtmRFJ3PUjcjmj4K6U8zhjD5oMneH3DIT7Yls/ZymoGxYdz/UW9uHpUIj266pAS3qbhr5RqVcVllXywLZ/XNhwkPfcUQQF+XDasJzdc1ItxKZH6a8BLNPyVUm1mR94pXt9wiHe3HKa4rIrUmFBuGpfMNaOTdIC5Nqbhr5Rqc2crqlmUkc+r6w+y6cAJgvz9mDs0npvGJzNefw20CQ1/pZRXZR0p5tX1B3lncy6ny6roGxPKTeN7c+1oPTbQmjT8lVLtwtmKaj5Mz+OV9QfZcvAkwQF+LBiewM0TknU4iVag4a+Uand25J3ilXUHeW/LYUorqhnSsxu3TOjNlSMT9LwBD9HwV0q1WyXlVby/9TAvrz1IZv5pwoMDuGZ0IrdM6E3/OD2LuCU0/JVS7Z49b+AkL689wKL0fCqqa5iQGsk3J/Zh9pA4HVPoAmj4K6U6lGMl5byxMZeX1x7g8MmzxHUL5qZxvblxXC9iu+kIo+7S8FdKdUjVNYZVWQW8+OUBPt1dSICfMG9YT26d2JsxvSP0AHETPBX+bh2BEZG5wMOAP/C0MebBetb5OnA/YIBtxpibWlqcUqrz8fcTZg6OY+bgOHKKSnl57QHe2HiID7blkZbQjVsn9eGKEQk6+1gra3LPX0T8gd3AbCAX2ADcaIzZ6bJOf+AN4BJjzAkRiTXGFDT2vLrnr5Sqdaaiine3HOaFL/az+2gJkaFB3DiuF7dM6E3P7l28XV670mbNPiIyEbjfGDPHuf1zAGPMn1zW+Quw2xjztLsvrOGvlKrLGMOXe4/x/Bf7+STzKCLC3KHxfGtSH20ScrRls08icMjldi4wvs46A5yi1mCbhu43xiyt+0QicidwJ0BycvKF1KuU6sREhEn9opnUL5pDx8/w0toDvLb+IIvS8xmW2J1vXdyHBcMTCArQXkIt5c4WrO+rtu7PhQCgPzAduBF4WkR6/MeDjHnSGDPWGDM2JiamubUqpXxIr8iu3Dd/MGvvm8nvrhrKmYoqfvzGNi7+8wr+b/kejpdWeLvEDs2d8M8FerncTgLy6lnnfWNMpTEmB8jCfhkopVSLdA0K4BsTevPxf0/j+W9dxOCe3fjfj3cz8U/L+fk76ew5WuztEjskd5p9NgD9RSQFOAzcANTtyfMedo//eRGJxjYD7fNkoUop3+bnJ0wfGMv0gbHsOVrMs2v2887mXF5df4hpA2K4Y0oKk/tF63EBN7nVz19E5gP/wLbnP2uM+YOI/BbYaIxZKHZr/y8wF6gG/mCMea2x59QDvkqpljpeWsG/1x7ghS8PUFRSzqD4cO6YksoVIzrvcQE9yUsppRzlVdW8vzWPZz7PIetoMbHhwdx2cR9uHt+b7l0CvV2eR2n4K6VUHcYYPttTxNOf7+PzPUWEBvlz/UXJ3D65D0kRXb1dnkdo+CulVCN25J3i6c9z+GBbHga4YkQCd05NZXDPbt4urUU0/JVSyg15J8/y7OocXl1/kNKKaqYNiOGuaX2ZkNoxp53U8FdKqWY4daaSl9cd4Lk1ORSVVDCyVw/umtaXS4fE4efXcb4ENPyVUuoClFVW8/bmXJ74dB8Hj5+hb0wod03ry1WjEjvE/AIa/kop1QJV1TUs2X6Ef63aS2b+aRK6h/CdqanccFEyXYLa74iiGv5KKeUBxhhWZRXyr1XZbNh/gqjQIL49JYVvTOhNeEj76yaq4a+UUh62Puc4/1yZzWe7C+kWEsBtF6dw+8V96NE1yLuFVZbBif1wfB8y+LK2m8xFKaV8wbiUSF5MGUd67kkeXZnNI8v38Mzn+/jGxD7cMSWF6LDg1nvxmmo4dQiOZUNRtv17LBuO7bX3/8d4mi2je/5KKdWAXUdO8+jKvXyYnkdwgB+3jO/NndNSiQ1vwZzDFWfg2B4o2gOFWVC0214/lg3V5V+tF9wNovpBVF+I7Hvur/Qaq80+SinVFvYWlvDoimze23qYQH8/bhqfzH9N69v4xPPlJVCUBQW7oHCXDfrCXXDyIOf24sUPIvpAVH+Irr0MsKEfGgP1nIegbf5KKdXG9heV8ujKbN7ZcpgAP7FfApN7EVt+EAp2OpdM+/fkwa8e6B9kQz16AMQMgpgBED3Q7s0HNK8pqU0ncFdKKZ9nDH2CTvHQyALu655Bzo71hG7IImJjHki1XccvwO7FJ46FUd+E2EEQM9ju3fu3r7htX9UopVR7UF1pm2mOZMDR7XAkHY5sh7PHAYgAIroncyZ1IJ+VTGPhkQj2STKTx07gOzMGERnq5d5BbtDwV0r5tsqzcHQH5G+F/G2Qn26bbmoPvgaEQOwQGLwA4oZB/FCIS4OQ7nQFZgKpRaU8snwPj685xIvr87h9cgp3TElt18NJa5u/Usp3VJTavfm8rV+FfWEWGKfZpksExA+HnsMhfgTED7MHX91ssskuKObvn+xhUXo+3UIC+O60vtw2qQ+hwZ7bz9YDvkop1Ziqcttkc3gz5G2xl8JdYGrs8tBYSBgFPUd8demeVG8Pm+bamXeav328m08yjxIdFsTdM/px0/hkggNaPmyEhr9SStWqqbH95A9v+upyJANqKu3yrlGQMNqGfcJI+ze8p0eCvjFbDp7goWVZfLH3GIk9uvDDmf25ZnQiAS0YQE7DXynlu84ch9yNkLsBDm+E3E1QfsouCwqz4Z442gZ+4mjo3qvVg74xq/cU8dCyXWzLPUW/2DB+Omcglw6Ju6D5BDT8lVK+oaba9ps/tN6G/aH1cHyvXSZ+EJsGSWMhcYz9Gz0A/NrfqJzGGJZuP8JDy7LYV1TKqOQe/HzeYMalRDbreTT8lVKdU9lpJ+TX2UvuJqgotstCY6HXOBtlDO6zAAAXtUlEQVTySRfZPfygUO/W20xV1TW8uSmXf3yym6Ony5k1OI6fzRtIv9hwtx6v4a+U6hxO5cLBtXDwSzi4zh6kxdi9+rg06DXeuYyDHr292nzjSWcrqnl2TQ6PrdrLmYoqrr8omf+e3b/JcYM0/JVSHY8xdiCzA2vgwJc28E8dssuCwuzefPIEG/ZJYyHYvb3hjux4aQWPLN/Dy2sPEBTgx3en9uU7U1PoGlR/91ANf6VU+1dTY/fkD6xxLl/AmWN2WWgs9J4IyZNs4McNbXdDILSlnKJS/rJ0F0u2HyGuWzD3XjqQa0cn/cf8whr+Sqn2p6bahv3+1fZyYA2UOb1wevSG3hdD70n2EpnaaZpwPGnTgeP87sNMth46ydDEbvzysiFMSI06t1zDXynlfTU1ULADcj6H/Z+fH/aRfaHPxdB7sv3bPcm7tXYgNTWGD9Lz+POSXeSdKmNuWjz3zR9MclRXHdVTKeUFxtiTqXI+hZzPbOg7g50RmQpDroQ+U6DPZOiW4N1aOzA/P+HKkYnMSYvnqc/28a9Ve1mxq4A7pqR47DU0/JVSjTudb8N+3yrY9ykU59n7uyXBwHk27FOm6J59KwgJ9Of7M/vztbG9+MvSXfxr1V6PPbc2+yilzldebNvr962yl8Jd9v4ukZAyFVKn27/aZt/mthw8wejekdrso5TygJpqO8rl3uWwd4U9waqmCgK62AOzI2+G1Gl2OGO/Cx+TRrXcqOQIjz2Xhr9Svuh0HmQvh+xP7N592UlA7FDGk74PqTNsX/vAFkxUrto1DX+lfEFVuT2hKvsTG/oFO+394T1h0ALoO8M254RGe7NK1YY0/JXqrE4cgOyPYc8ntmdOZamdSDx5Isz+HfSbBbGDtd3eR2n4K9VZVFfavfvdy2DPx1CUZe/v0RtG3gj9ZtteOR1sIDTVOjT8lerISgrt3v3upbB3JZSftnv3vSfBmNug/2w7DaHu3as63Ap/EZkLPAz4A08bYx5sYL3rgDeBi4wx2o9TKU8zxg6fsHspZC21M1ZhbNt92tUwYA6kTIPgMG9Xqtq5JsNfRPyBR4HZQC6wQUQWGmN21lkvHPgBsK41ClXKZ1WV2373WUts6NeOgpkwGmbcZwM/frju3atmcWfPfxyQbYzZByAirwFXAjvrrPc74C/AvR6tUClfdOa4bbfPWmR751SUQGBX2wVz2v+D/pdCeJy3q1QdmDvhnwgccrmdC4x3XUFERgG9jDEfikiD4S8idwJ3AiQnJze/WqU6s5MHYddi2PWhHfrYVENYPAy7DgZeZg/WBnbxdpWqk3An/Ov7LXluTAgR8QP+DtzW1BMZY54EngQ7vIN7JSrVSRlj+9tnfmgD/0i6vT9mEEz+kQ38hFF6Vq1qFe6Efy7Qy+V2EpDncjscGAqscmaijwcWisgVetBXqTpqauxB2sz3beifyAHETlE4+3cw6DKI6uvtKpUPcCf8NwD9RSQFOAzcANxUu9AYcwo4d1qgiKwC7tXgV8pRXWXHuc/8wO7hF+eDX6AdHO3iH9g9fG2/V22syfA3xlSJyD3AMmxXz2eNMTtE5LfARmPMwtYuUqkOp6rCnlWb+T7sWmSnLgzoAv1nweAr7AHbLj28XaXyYW718zfGLAYW17nv1w2sO73lZSnVAVVVwL6VsOM920un7BQEhduumEOutMMpBHX1dpVKAXqGr1Itcy7w37U9dcpPQXB3GDTfBn7qDB0ZU7VLGv5KNVd1pZ3Rasc7tg2/rDbwL4O0q+zomAHB3q5SqUZp+Cvljppqe5bt9rchcyGcPQHB3ZzAv9ru4QcEebtKpdym4a9UQ2pq7KxW29+y7filBRAUZuetTbsG+s3UPXzVYWn4K+WqduC0jLfsXv6pQxAQYnvnDL3W/tWDtqoT0PBXCuB4jt3Dz3jLTljuF2Cbci75JQycDyHdvF2hUh6l4a98V2kRbH8HMt6E3PX2vuSJcNnfYMhVEBrl3fqUakUa/sq3VJyBrMWQ/rodLdNUQ2wazLofhl4HPXo19QxKdQoa/qrzq6mG/Z/DttdtT52KEuiWCJO+D8O/DnFp3q5QqTan4a86r4JM2PYapL8BxXm2a2ba1Tbwe0/W0TKVT9PwV51LaZFtw9/2KuRvA/G389jO+YPtoqnj4SsFaPirzqCqAvYsg62v2r81VXZaw7kP2nb8sBhvV6hUu6PhrzomY+zkJ1tfsc06Z49DWBxM+C8YcRPEDfF2hUq1axr+qmMpLbJhv/Xf9mQs/yA7xMKIm6DvJeCvH2ml3KH/U1T7V10Fe1fAlhchaynUVNrpDef/1Z512zXS2xUq1eFo+Kv269he2PKyPXhbnA9do2HcnTDqFm3WUaqFNPxV+1JxxvbF3/wSHFgN4gf9ZsP8h6D/HB05UykP0fBX7UN+Omx+AdLftBOiRKTAJb+CkTdBtwRvV6dUp6Phr7yn7LQdTG3TC5C/FfyD7exXo7+hJ2Ep1co0/FXbMgYOb4ZNz9lB1SpL7dg68/5iz7ztEuHtCpXyCRr+qm2UnYaMN2DT83AkAwK72p46Y26DxDEg4u0KlfIpGv6qdeVtgY3PQsbbdi8/fpgdMnnY13SMfKW8SMNfeV5FqZ0Fa+OzNvxr9/LHfgsSRutevlLtgIa/8pyCXbDxGTuSZvlpiBkM8x6CEddDSHdvV6eUcqHhr1qmqgJ2fQAbnrX98v2D7CxYY2+H5Am6l69UO6Xhry7MqcO2x86mF6C0AHr0hlkP2LNvQ6O9XZ1Sqgka/sp9xkDOZ7DhKdi1GEwN9L8ULroD+s3SfvlKdSAa/qpp5cW2HX/9U1CUBV0iYdI9tmknoo+3q1NKXQANf9Wwoj028Le+AhXFdiTNqx6DtGsgMMTb1SmlWkDDX52vpgayP4Z1j9thlP2D7Ly34+6EpLHerk4p5SEa/soqOwVb/g3rn4QTORDeE2b8EsbcCmGx3q5OKeVhGv6+rmgPrHvCNu1UlkKvCTDzVzD4CvAP9HZ1SqlWouHvi4yxTTprH7NNPP5B9gzc8d+17fpKqU5Pw9+XVJyB9Ndt6BdlQWgsTP+57bWjTTtK+RS3wl9E5gIPA/7A08aYB+ss/zFwB1AFFAK3G2MOeLhWdaFO59leO5ueg7MnIH44XP2EPZAbEOzt6pRSXtBk+IuIP/AoMBvIBTaIyEJjzE6X1bYAY40xZ0Tkv4C/ANe3RsGqGfK2wpePwo53oKYaBl0GE74HvSfpsAtK+Th39vzHAdnGmH0AIvIacCVwLvyNMStd1l8L3OLJIlUz1NTA7qU29A+shqAwewbu+LsgMsXb1Sml2gl3wj8ROORyOxcY38j63waW1LdARO4E7gRITk52s0TlloozsO0V+PJfcHwvdEuCS38Po7+pI2oqpf6DO+FfX/uAqXdFkVuAscC0+pYbY54EngQYO3Zsvc+hmqmkwPbN3/AMnD1ux8u/7lkYfCX46/F8pVT93EmHXKCXy+0kIK/uSiIyC/gFMM0YU+6Z8lSDCrPgi/+zvXeqK2HgfJj0fR1GWSnlFnfCfwPQX0RSgMPADcBNriuIyCjgCWCuMabA41Uqyxg4sMaG/u6lEBBih1CecDdE9/N2dUqpDqTJ8DfGVInIPcAybFfPZ40xO0Tkt8BGY8xC4CEgDHhT7F7nQWPMFa1Yt2+pqYbMD2DNw5C3GbpG2f75F92hY+crpS6IW43CxpjFwOI69/3a5fosD9elACrPwtZ/wxf/tOPtRKbayc9H3gSBXbxdnVKqA9Mjgu3RmeP2AO66x+FMkT2IO/sBGLQA/Py9XZ1SqhPQ8G9PTh22/fM3PW8HWes3Gy7+IfSZrAdxlVIepeHfHhTutu356a/bqRGHXQeTfgDxQ71dmVKqk9Lw96bcTbD6b7Brke25M/Z2mHg3RPT2dmVKqU5Ow7+tGQP7VtnQz/kMQnrA1J/a4ZS1545Sqo1o+LeVmhrIWgSf/y/kbYGweDv8wpjbIDjc29UppXyMhn9rq66C7W/B53+zY+hHpMDlD8OIG3U4ZaWU12j4t5bKMjvQ2up/wMkDEJsG1z4DQ67SMXeUUl6nKeRpFaW2q+aaR6DkCCSOhXl/hv5zwM/P29UppRSg4e85Zadhw1O2n/6ZY9BnClzzBKRM0z76Sql2R8O/pc4ct2firnscyk7ZE7Om/hSSG5vyQCmlvEvD/0KVFsGX/7Rz41aU2KEXpv4UEkZ6uzKllGqShn9zFR+FLx6Bjc/agdfSroap90JcmrcrU0opt2n4u+t0vh2CYdNzUF0Bw74GU+6FmAHerkwppZpNw78pp/Ng9d9h0wtQU2X750/5MUT19XZlSil1wTT8G3Iq14b+5hftYGsjboQpP4HIFG9XppRSLabhX1fd0B95sw19HWxNKdWJaPjXOnXYDrZWG/qjboHJP9bQV0p1Shr+p/Nt6G96/qvQn/IT6JHs7cqUUqrV+G74Fx+xzTsbnwNTbefFnXKv7ukrpXyC74V/SSGs+QdseBqqK2HkjfbkrIg+3q5MKaXajO+E/5njtp/++iehqgyGX29DX7tsKqV8UOcP/7Mn7WBrax+zwzAMvRam/wyi+3u7MqWU8prOG/7lxXawtS/+zw64NuRKmP5ziB3s7cqUUsrrOl/4V5617fmr/26HVh4wD2bcBz2He7sypZRqNzpP+FdVwOYX4LO/2klUUqfDJb+CpLHerkwppdqdjh/+NdWQ/jqs+hOcPAi9JsB1z0Cfyd6uTCml2q2OG/7GQOZCWPEHOzF6zxFw2d+h30ydOUsppZrQ8cLfGNi7HJb/DvK3QvRA+PpLMPhyDX2llHJTxwr/g+tg+QNwYI0dfuGqx2x/fT9/b1emlFIdSscI/yPbYcXvYPdSCI2F+X+F0bdCQJC3K1NKqQ6pfYf/8RxY+UfIeBOCu8HMX8P4uyAo1NuVKaVUh9Y+w7+kAD79ix1p0y8ALv6hvXSN9HZlSinVKbSv8C87bSdH//JfdvydMbfC1P+Bbj29XZlSSnUq7SP8q8phwzPw2UNw9jikXW1P0NJB15RSqlW4Ff4iMhd4GPAHnjbGPFhneTDwIjAGOAZcb4zZ3+QT11Tb9vwVf4BTB+1ZubPuh4RRzXgLSimlmqvJ8BcRf+BRYDaQC2wQkYXGmJ0uq30bOGGM6SciNwB/Bq5v9InLT8MTU+HodnuC1hUPQ99LLviNKKWUcp87e/7jgGxjzD4AEXkNuBJwDf8rgfud628B/xQRMcaYBp/12F6o6ALXPgNp14Cf34XUr5RS6gK4E/6JwCGX27nA+IbWMcZUicgpIAoocl1JRO4E7nRulsuP0rfD1y6k7rYUTZ330U5pnZ7TEWoErdPTOkqdAz3xJO6Ef31jJtTdo3dnHYwxTwJPAojIRmNMux9yU+v0rI5QZ0eoEbROT+tIdXriedxpa8kFerncTgLyGlpHRAKA7sBxTxSolFLK89wJ/w1AfxFJEZEg4AZgYZ11FgK3OtevA1Y02t6vlFLKq5ps9nHa8O8BlmG7ej5rjNkhIr8FNhpjFgLPAC+JSDZ2j/8GN177yRbU3Za0Ts/qCHV2hBpB6/Q0n6pTdAddKaV8j/avVEopH6Thr5RSPqhVwl9E5opIlohki8jP6lkeLCKvO8vXiUgfl2U/d+7PEpE5rVGfmzX+WER2iki6iCwXkd4uy6pFZKtzqXvwu63rvE1ECl3qucNl2a0isse53Fr3sW1c599datwtIiddlrXl9nxWRApEZHsDy0VEHnHeR7qIjHZZ1ibb040ab3ZqSxeRL0RkhMuy/SKS4WxLj3QJbEGd00XklMu/7a9dljX6eWnjOn/qUuN25/MY6Sxry+3ZS0RWikimiOwQkR/Ws47nPp/GGI9esAeF9wKpQBCwDRhSZ53vAY87128AXneuD3HWDwZSnOfx91KNM4CuzvX/qq3RuV3i6ZpaUOdtwD/reWwksM/5G+Fcj/BWnXXW/z6240Cbbk/ntaYCo4HtDSyfDyzBnrsyAVjnhe3ZVI2Tal8bmFdbo3N7PxDdTrbldODDln5eWrvOOuteju2t6I3t2RMY7VwPB3bX8//dY5/P1tjzPzcchDGmAqgdDsLVlcALzvW3gJkiIs79rxljyo0xOUC283xtXqMxZqUx5oxzcy32/Ia25s62bMgc4GNjzHFjzAngY2BuO6nzRuDVVqqlUcaYz2j8HJQrgReNtRboISI9acPt2VSNxpgvnBrAe59Nd7ZlQ1ryuW62Ztbpzc9mvjFms3O9GMjEjp7gymOfz9YI//qGg6j7Bs4bDgKoHQ7Cnce2VY2uvo39tq0VIiIbRWStiFzVCvXVcrfOa52fgG+JSO0JeW21LZv1Wk7zWQqwwuXuttqe7mjovbTl9myOup9NA3wkIpvEDqfibRNFZJuILBGRNOe+drktRaQrNjDfdrnbK9tTbFP4KGBdnUUe+3y2xnj+LRkOwq1hIjzA7dcRkVuAscA0l7uTjTF5IpIKrBCRDGPMXi/V+QHwqjGmXETuwv6iusTNx3pKc17rBuAtY0y1y31ttT3d4e3PpttEZAY2/Ce73H2xsy1jgY9FZJez5+sNm4HexpgSEZkPvAf0px1uS8flwBpjjOuvhDbfniIShv0C+pEx5nTdxfU85II+n62x59+S4SDceWxb1YiIzAJ+AVxhjCmvvd8Yk+f83Qeswn5Dt4Ym6zTGHHOp7SnsnApuPbYt63RxA3V+Vrfh9nRHQ++lLbdnk0RkOPA0cKUx5ljt/S7bsgB4l9ZpNnWLMea0MabEub4YCBSRaNrZtnTR2GezTbaniARig//fxph36lnFc5/PVjhoEYA92JDCVwdz0uqsczfnH/B9w7mexvkHfPfROgd83alxFPagVP8690cAwc71aGAPrXSwys06e7pcvxpYa746AJTj1BvhXI/0Vp3OegOxB9DEG9vT5TX70PBByss4/4Da+rbenm7UmIw9Hjapzv2hQLjL9S+AuV7clvG1/9bY0DzobFe3Pi9tVaezvHYHNNRb29PZNi8C/2hkHY99PlvrTczHHqneC/zCue+32D1ogBDgTecDvB5IdXnsL5zHZQHzWnFDN1XjJ8BRYKtzWejcPwnIcD6wGcC3W/lD21SdfwJ2OPWsBAa5PPZ2ZxtnA9/yZp3O7fuBB+s8rq2356tAPlCJ3Vv6NnAXcJezXLCTF+116hnb1tvTjRqfBk64fDY3OvenOttxm/OZ+IWXt+U9Lp/Ntbh8WdX3efFWnc46t2E7m7g+rq2352RsU026y7/t/Nb6fOrwDkop5YP0DF+llPJBGv5KKeWDNPyVUsoHafgrpZQP0vBXSikfpOGvfIZzin5Qnfv2OyceXcjz3S8i9zrXQ0TkYxH5TROPue9CXkspT9PwVz7BGSvlsLEDiXn6uYOwZ2VuMsY80MTqGv6qXdDwVx2KiPQRkV0i8rQz9vq/RWSWiKxxxjFv6PT7ecDSRp63i4gsFZHvOLd/5bzOxyLyau0efj0CsKNS7jHG/Mzl+d5zfmnsqB0QTEQeBLo4Y8P/+0Lev1KeouGvOqJ+wMPAcGAQcBP27Mh7aXjPei4Nh38YdoC8V4wxT4nIWOBa7BAf12AH9mvI/wBVxpgf1bn/dmPMGOexPxCRKOfL4awxZqQx5uam3qRSrUnDX3VEOcaYDGNMDfa0++XGnqqegR3D5TxOs0ySsQPH1ed94DljzIvO7cnA+8aYs8aOq/5BI7Wsxg5bPKDO/T8QkdphDXphR7NUqt3Q8FcdUbnL9RqX2zXUP0z5FGxIN2QNMM+ZUAjqHx63IZ8BPwKWiEgC2OkLgVnARGPMCGALdjwrpdoNDX/lC+Zy/oQndf0aOAb8y7m9Grjc6cEThh1JsUHGmLeBh4ClItIDO0LkCWPMGREZhB19sValM2yvUl6l4a98wXTg0ybW+RF2RrG/GGM2AAuxozm+A2zEzjbXIGPM4866C7FzEgSISDrwO2zTT60ngXQ94Ku8TUf1VJ2aiCQBTxlj5jXzcWHGzkDVFdu0c6dx5ldVqjPQ8FeqHiLyCjAE21b/gjHmT14uSSmP0vBXSikfpG3+SinlgzT8lVLKB2n4K6WUD9LwV0opH6Thr5RSPuj/A08riIoLChAFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1645e7d20b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1645ed0f3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy import integrate\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "k = 10 # L^2 kg^-1 min^-1\n",
    "ka = 1 # L/mol\n",
    "kb = 2 # L/mol\n",
    "kc = 20 # L/mol\n",
    "alpha = 0.4 # kgKat^-1\n",
    "na0 = 1.5 # mol/min\n",
    "ca0 = 1 # mol/L\n",
    "cb0 = 1 # mol/L\n",
    "ya0 = ca0/(ca0+cb0)\n",
    "ea = (1+1-1-1)*ya0\n",
    "\n",
    "m = np.linspace(0,2,100) # 0-2kgKat\n",
    "\n",
    "def dy_dm(y, t0):\n",
    "    p_d_p0 = y[0]\n",
    "    ua = y[1]\n",
    "    ca = ca0*(1-ua)/(1+ea*ua)*p_d_p0\n",
    "    cb = ca\n",
    "    dp_d_p0_dm = -alpha/2. * (1+ea * ua)/(p_d_p0)\n",
    "    dua_dm = k/na0*(ca)**2 /(1+ka*ca)\n",
    "    return np.array([dp_d_p0_dm, dua_dm])\n",
    "\n",
    "y, info = integrate.odeint(\n",
    "    dy_dm, np.array([1.0,0.0]), m, \n",
    "    full_output=True)\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = plt.subplot(111)\n",
    "ax.plot(m, y[:,0], label='$P/P_0$')\n",
    "ax.plot(m, y[:,1], label='$U_A$')\n",
    "ax.legend()\n",
    "ax.set_title('$r_1 = k c_A c_B/(1+K_A c_A)$')\n",
    "ax.set_xlabel('m / kg Kat')\n",
    "ax.set_xlim([0,2])\n",
    "ax.set_ylim([0,1.]);\n",
    "\n",
    "def dy_dm(y, t0):\n",
    "    p_d_p0 = y[0]\n",
    "    ua = y[1]\n",
    "    ca = ca0*(1-ua)/(1+ea*ua)*p_d_p0\n",
    "    cb = ca\n",
    "    cc = ca0*(0+ua)/(1+ea*ua)*p_d_p0\n",
    "    cd = ca0*(0+ua)/(1+ea*ua)*p_d_p0\n",
    "    dp_d_p0_dm = -alpha/2. * (1+ea * ua)/(p_d_p0)\n",
    "    dua_dm = k/na0*(ca)**2 /(1+ka*ca+kc*cc)\n",
    "    return np.array([dp_d_p0_dm, dua_dm])\n",
    "\n",
    "y, info = integrate.odeint(\n",
    "    dy_dm, np.array([1.0,0.0]), m, \n",
    "    full_output=True)\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = plt.subplot(111)\n",
    "ax.plot(m, y[:,0], label='$P/P_0$')\n",
    "ax.plot(m, y[:,1], label='$U_A$')\n",
    "ax.legend()\n",
    "ax.set_title('$r_2 = k c_A c_B/(1+K_A c_A + K_C c_C)$')\n",
    "ax.set_xlabel('m / kg Kat')\n",
    "ax.set_xlim([0,2])\n",
    "ax.set_ylim([0,1.]);\n",
    "\n",
    "def dy_dm(y, t0):\n",
    "    p_d_p0 = y[0]\n",
    "    ua = y[1]\n",
    "    ca = ca0*(1-ua)/(1+ea*ua)*p_d_p0\n",
    "    cb = ca\n",
    "    cc = ca0*(0+ua)/(1+ea*ua)*p_d_p0\n",
    "    cd = ca0*(0+ua)/(1+ea*ua)*p_d_p0\n",
    "    dp_d_p0_dm = -alpha/2. * (1+ea * ua)/(p_d_p0)\n",
    "    dua_dm = k/na0*(ca)**2 /(1+ka*ca+kb*cb)**2\n",
    "    return np.array([dp_d_p0_dm, dua_dm])\n",
    "\n",
    "y, info = integrate.odeint(\n",
    "    dy_dm, np.array([1.0,0.0]), m, \n",
    "    full_output=True)\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = plt.subplot(111)\n",
    "ax.plot(m, y[:,0], label='$P/P_0$')\n",
    "ax.plot(m, y[:,1], label='$U_A$')\n",
    "ax.legend()\n",
    "ax.set_title('$r_3 = k c_A c_B/(1+K_A c_A + K_B c_B)^2$')\n",
    "ax.set_xlabel('m / kg Kat')\n",
    "ax.set_xlim([0,2])\n",
    "ax.set_ylim([0,1.]);\n",
    "\n",
    "def dy_dm(y, t0):\n",
    "    p_d_p0 = y[0]\n",
    "    ua = y[1]\n",
    "    ca = ca0*(1-ua)/(1+ea*ua)*p_d_p0\n",
    "    cb = ca\n",
    "    cc = ca0*(0+ua)/(1+ea*ua)*p_d_p0\n",
    "    cd = ca0*(0+ua)/(1+ea*ua)*p_d_p0\n",
    "    dp_d_p0_dm = -alpha/2. * (1+ea * ua)/(p_d_p0)\n",
    "    dua_dm = k/na0*(ca)**2 /(1+ka*ca+kb*cb+kc*cc)**2\n",
    "    return np.array([dp_d_p0_dm, dua_dm])\n",
    "\n",
    "y, info = integrate.odeint(\n",
    "    dy_dm, np.array([1.0,0.0]), m, \n",
    "    full_output=True)\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = plt.subplot(111)\n",
    "ax.plot(m, y[:,0], label='$P/P_0$')\n",
    "ax.plot(m, y[:,1], label='$U_A$')\n",
    "ax.legend()\n",
    "ax.set_title('$r_3 = k c_A c_B/(' +\n",
    "             '1+K_A c_A + K_B c_B + K_C c_C)^2$')\n",
    "ax.set_xlabel('m / kg Kat')\n",
    "ax.set_xlim([0,2])\n",
    "ax.set_ylim([0,1.]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 11.5.b Froment Bischoff\n",
    "Maleinsäure-Herstellung aus Benzol. Reaktion pseudo-1. Ordnung wegen Sauerstoff-Überschuss.\n",
    "\n",
    "$r_A=k p_B^{\\circ}p$\n",
    "\n",
    "$ln(k) =19.837-\\frac{13.636}{T}$\n",
    "\n",
    "Anmerkung: Nach Notation dieses Buches(S. XVII, oder S. 14) bestehen die folgenden Einheiten: $k_A[=] \\frac{kmol}{kgKat\\cdot h}\\cdot atm^{-2}$,\n",
    "$r_A[=] \\frac{kmol}{kgKat\\cdot h} $\n",
    "\n",
    "Kontinuität, Energie:\n",
    "\n",
    "$u_s\\frac{dp}{dz}+\n",
    "\\frac{M_m p_t \\rho_B}{\\rho_g}k p_B^{\\circ}p=0$\n",
    "\n",
    "$u_s \\rho_g c_p \\frac{dT}{dz}-\n",
    "(-\\Delta H)\\rho_B k p_B^{\\circ}p + \n",
    "\\frac{4 U}{d_t}(T-T_r)=0$\n",
    "\n",
    "Randbedingungen: $p=p_0, z=0; T=T_0=T_r, z=0$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Kurze Anmerkung zur Nomenklatur bei Froment-Bischoff:*\n",
    "\n",
    "| Name | Beschreibung | Einheiten |\n",
    "| - | - | - |\n",
    "| $\\rho_B$ | Katalysator Feststoffdichte | $\\frac{kg Kat}{m^3}$ |\n",
    "| $u_S$ | Oberflächenspezifischer Volumenstrom | $\\frac{m^3}{m^2 h}$ |\n",
    "| $\\rho^{\\circ}$ | Dichte des Lösungsmittels | $\\frac{kg}{m^3}$ |\n",
    "| *Tr* | Temperatur der Umgebung | °C |\n",
    "| $d_t$ | Innerer Rohrdurchmesser | cm |\n",
    "| $M_m$ | Mittlere Molmasse | $\\frac{g}{mol}$ |\n",
    "\n",
    "d. h., um Koordinate $z$ in Masse Kat $m$ umzuwandeln braucht man (s. o). \n",
    "\n",
    "$m=\\underbrace{(1-\\phi)A_c\\cdot z}_{Volumen}\\cdot  \\rho_c = \\pi/4 d_t^2 z \\cdot \\rho_B$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- *Vorgaben* und Stoffdaten:\n",
    "\n",
    "Betriebsdruck: atmosphärisch, 1 atm\n",
    "\n",
    "Betriebstemperatur (335-415°C): 352°C\n",
    "\n",
    "Eintrittsgaszusammensetzung (1mol-% Benzol in Luft):\n",
    "\n",
    "| Komponente | mol% | $\\frac{Mm}{g/mol}$ |\n",
    "| - | - | - |\n",
    "|Benzol| 0.99% | 78 |\n",
    "|O2| 20.79% | 32 | \n",
    "|N2| 77.23% | 28 |\n",
    "|Ar| 0.99% | 40 |\n",
    "\n",
    "\n",
    "Gesamtkoeffizient\n",
    "\n",
    "$\\frac{1}{U}=\\frac{1}{\\alpha_i}+\n",
    "\\frac{d}{\\lambda}\\frac{A_b}{A_m}+\n",
    "\\frac{1}{\\alpha_u}\\frac{A_b}{A_u}$\n",
    "\n",
    "**Froments Korrelation** von Nusselt und Reynoldszahl:\n",
    "$\\frac{\\alpha_i d_p}{\\lambda_g}= \\frac{\\alpha_i^0 d_p}{\\lambda_g}\n",
    "+0.033\\left(\\frac{c_p \\mu}{\\lambda_g}\\right)\\left(\\frac{d_p G}{\\mu}\\right)$\n",
    "\n",
    "Statischer Beitrag: $\\alpha_i^0=\\frac{2,44 \\lambda_e^0}{d_t^{4/3}}$\n",
    "\n",
    "Aber, $\\lambda_e^0$ muss untersucht werden.\n",
    "\n",
    "**Levas Korrelation** für:\n",
    "\n",
    "Heizung: $\\frac{\\alpha_i d_t}{\\lambda_g}=\n",
    "0,813\\left(\\frac{d_p G}{\\mu}\\right)^{0,9}\n",
    "e^{-6d_p/d_t}$\n",
    "\n",
    "Kühlung: $\\frac{\\alpha_i d_t}{\\lambda_g}=\n",
    "3,50\\left(\\frac{d_p G}{\\mu}\\right)^{0,7}\n",
    "e^{-4,6d_p/d_t}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Eigenschaften der Luft-Benzol Mischung bei Betriebsbedingungen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prozessstrom, Luft mit verdünntem o-Xylen-Anteil\n",
      "mm = 29.4466 g/mol\n",
      "cv_g = 0.769624 kJ/kg/K (VDI-Wärmeatlas)\n",
      "cp_g = 1.06242 kJ/kg/K ... = (cv_g*M+R)/M Idealgas\n",
      "rho_g = 0.574061 kg/m^3 ... Idealgas\n",
      "Bird Tabelle E.1: \n",
      "epsilon/k = [  99.8  113.   122.4  387. ] K\n",
      "sigma = [ 3.667  3.433  3.432  5.443] Angstrom\n",
      "Bird Tabelle E.2: \n",
      "Omega_mu=Omega_k = [ 0.88999534  0.91051159  0.9235125   1.2750801 ] \n",
      "Bird Gl. 1.4-14, 1.4-15, 1.4-16, 9.3-13: \n",
      "mu = 3.04203e-05 Pa s\n",
      "k = 0.0429474 W/m/K\n",
      "k = lambda_g = 36.9528 kcal/m/h/°C\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.interpolate import interp1d\n",
    "t0 = 352 + 273.15 # °K (335-415°C Betriebstemperatur)\n",
    "t = t0\n",
    "p = 1 # atm\n",
    "# Ordnung für die Eigenschaften: N2, O2, Ar, Benzol\n",
    "komponente = np.array(['N2', 'O2', 'Ar', 'Benzol'])\n",
    "y_i = np.array([78,21,1,1])/sum(\n",
    "    np.array([78,21,1,1], dtype=float))\n",
    "mm_g = np.array([28, 32, 40, 78.11]) # g/mol\n",
    "# IG-Eigenschaften\n",
    "rho_g = 101325./(8.314*t)*mm_g/1000. # kg/m^3\n",
    "# VDI Wärmeatlas - Cv bei 352°C\n",
    "# Gasen bei 352°C\n",
    "cv_g = np.array([\n",
    "    (0.7640-0.7500)/(400-350)*(352-400)+0.7640 ,\n",
    "    (0.795-0.783)/(400-350)*(352-400)+0.795 ,\n",
    "    3/2*8.3145/40,\n",
    "    (2.212-1.991)/(400-300)*(352-400)+2.212 ,\n",
    "])\n",
    "# kJ/(kg K) = J/g/K\n",
    "cp_g = (8.3145+cv_g*mm_g)/mm_g # Nach Idealgasmodell\n",
    "# Lennard-Jones Parameter (Bird Tabelle E.1)\n",
    "l_j_epsilon_d_k = np.array([99.8,113,122.4,387.]) # K\n",
    "l_j_sigma = np.array([3.667,3.433,3.432,5.443]) # Angstrom\n",
    "k_t_d_e = t / l_j_epsilon_d_k\n",
    "# Stoßintegral (Bird Tabelle E.2)\n",
    "stossintegral_k_mu = interp1d(\n",
    "    [1.60,1.65,5.0, 6.0, 7.0],\n",
    "    [1.280,1.264,0.9268,0.8962,0.8727]\n",
    ")(k_t_d_e)\n",
    "konst_1 = 5 / 16 * np.sqrt(\n",
    "    1.3806e-23 * 1000 * 100**2 / 6.022e23 / np.pi\n",
    ") * (10**10 / 100)**2  # 1/cm/s\n",
    "konst_2 = (9 / 4 * 8.3145 + cv_g * mm_g\n",
    "          ) * 1 / 4.184 * konst_1 # cal/cm/s/K\n",
    "mu = konst_1 * np.sqrt(mm_g * t) / (\n",
    "    l_j_sigma**2 * stossintegral_k_mu)*100/1000. \n",
    "# g/cm/s * 100cm/1000g * 1kg/m = kg/m/s = Pa s\n",
    "k = konst_2 * np.sqrt(t / mm_g) / (\n",
    "    l_j_sigma**2 * stossintegral_k_mu\n",
    ") * 4.184 * 100 # W/m/K\n",
    "\n",
    "def phi_alpha_beta(mm_i, mu):\n",
    "    phi_ab = np.zeros([mm_i.size, mu.size])\n",
    "    for alpha in range(phi_ab.shape[0]):\n",
    "        for beta in range(phi_ab.shape[1]):\n",
    "            phi_ab[alpha, beta] = 1/np.sqrt(8)*(\n",
    "                1+mm_i[alpha]/mm_i[beta])**(-1/2.)*(\n",
    "                1+(mu[alpha]/mu[beta])**(1/2.)*(\n",
    "                    mm_i[beta]/mm_i[alpha]\n",
    "                )**(1/4.)\n",
    "            )**2\n",
    "    return phi_ab\n",
    "\n",
    "mu_mix = sum(y_i * mu / phi_alpha_beta(\n",
    "    mm_g,mu).dot(y_i))\n",
    "k_mix = sum(y_i * k / phi_alpha_beta(\n",
    "    mm_g,k).dot(y_i))\n",
    "\n",
    "# Eigenschaften als konstant für die Mischung angenommen\n",
    "rho_g = (sum(y_i * rho_g/mm_g)*sum(y_i * mm_g)).item()\n",
    "cp_g = (sum(y_i * cp_g/mm_g)*sum(y_i * mm_g)).item()\n",
    "cv_g = (sum(y_i * cv_g/mm_g)*sum(y_i * mm_g)).item()\n",
    "mm_g = sum(y_i * mm_g).item()\n",
    "k = k_mix\n",
    "mu = mu_mix\n",
    "lambda_g = k_mix\n",
    "\n",
    "output = [\n",
    "    'Prozessstrom, Luft mit verdünntem o-Xylen-Anteil',\n",
    "    'mm = ' + '{:g}'.format(mm_g) + ' ' + 'g/mol',\n",
    "    'cv_g = ' + '{:g}'.format(cv_g) + ' ' + 'kJ/kg/K' +\n",
    "    ' (VDI-Wärmeatlas)',\n",
    "    'cp_g = ' + '{:g}'.format(cp_g) + ' ' + 'kJ/kg/K' +\n",
    "    ' ... = (cv_g*M+R)/M Idealgas',\n",
    "    'rho_g = ' + '{:g}'.format(rho_g) + ' ' + 'kg/m^3' +\n",
    "    ' ... Idealgas',\n",
    "    'Bird Tabelle E.1: ',\n",
    "    'epsilon/k = ' + str(l_j_epsilon_d_k) + ' ' + 'K',\n",
    "    'sigma = ' + str(l_j_sigma) + ' ' +  'Angstrom',\n",
    "    'Bird Tabelle E.2: ',\n",
    "    'Omega_mu=Omega_k = ' + str(\n",
    "        stossintegral_k_mu) + ' ',\n",
    "    'Bird Gl. 1.4-14, 1.4-15, 1.4-16, 9.3-13: ',\n",
    "    'mu = ' + '{:g}'.format(mu) + ' ' + 'Pa s',\n",
    "    'k = ' + '{:g}'.format(k) + ' ' + 'W/m/K',\n",
    "    'k = lambda_g = ' + '{:g}'.format(\n",
    "        k*1/4.184*60**2) + ' ' + 'kcal/m/h/°C'\n",
    "]\n",
    "print('\\n'.join(output))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Berechnung vom Wärmeübergangskoeffizienten"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Kühlmittel: Wasser bei Sättigung bei 230°C (503.15K, 28bar) (VDI-Wärmeatlas)\n",
      "rho_l = 827.12 kg/m^3\n",
      "cp_l = 4.68318 kJ/kg/K\n",
      "eta_l = 0.0001162 Pa s\n",
      "Pr_l = 0.854831 \n",
      "Voll-ausgebildete turbulente Strömung:\n",
      "Re_l = 4.12263e+06 \n",
      "==>> G_l = 925257 kg/m^2/h\n",
      "==>> m_dot_l = 1.35251e+06 kg/h\n",
      "==>> u_s_l = 1118.65 m/h\n",
      "Nusselt-Zahl bei voll-ausgebildeter turbulenterStrömung (Gl. 26 Kap. G1 VDI-Wärmeatlas)\n",
      "xi_l = 0.00923257 \n",
      "Nu_l = 4835.36 \n",
      "Bezugslänge: Innendurchmesser des Rohrbündels mit 2500 Rohren, je 2,54cm\n",
      "d_i = 1.86389 m\n",
      "Wärmeübergangskoeffizient im Mantel\n",
      "alpha_o = 1420.97 kcal/h/m^2/°C\n"
     ]
    }
   ],
   "source": [
    "# Wasser als Kühlmittel: Gesättigte Flüssigkeit bei\n",
    "# 230°C, 27,968 bar\n",
    "rho_l = 827.12 # kg/m^3\n",
    "cp_l = 4.68318 # kJ/kg/K\n",
    "lambda_l = 636.6*1e-3 # W/m/K\n",
    "eta_l = 116.2*1e-6 # Pa s\n",
    "mu_l = eta_l\n",
    "pr_l = eta_l/(lambda_l/(cp_l*1000)) # [dimlos]\n",
    "d_i = 2.54*np.sqrt(2500)/2.6/np.sqrt(33*2)*31.0 / 100 #m\n",
    "\n",
    "# Wanddicke und Wärmeleitfähigkeit: St. 35.8. (1.0305)\n",
    "w_d = 0.133*1/12*30.48/100. # m\n",
    "lambda_m = (\n",
    "    (45-50)/(400-300)*(352-400)+45\n",
    ")*1/4.184/1000.*60**2 # kcal/h/m^2/K\n",
    "\n",
    "re_l = (\n",
    "    1/(1/82.7-1/88.4539 - w_d/lambda_m \n",
    "      )*1000*4.184/60**2 * \\\n",
    "    d_i/lambda_l/(pr_l**0.333)/0.026)**(1/0.8)\n",
    "xi_l = (1.8*np.log10(re_l)-1.5)**(-2.)\n",
    "nu_l = xi_l/8.*re_l*pr_l/(\n",
    "    1+12.7*np.sqrt(xi_l/8.)*(pr_l**(2/3.)-1)\n",
    ")*(1+(0.)**(2/3)) # d_i/l<<1 \n",
    "# (wesentlich höhere Länge als Durchmesser)\n",
    "nu_l = 0.026*re_l**0.8*pr_l**0.333*1**0.14 # Bird\n",
    "alpha_o = nu_l * lambda_l/d_i * \\\n",
    "    60**2 * 1/4.184 * 1/1000 # W/m/K * 1000cal/4184J *\n",
    "# 60^2s/h\n",
    "# Kühlmittel Massenstrom\n",
    "g_l =  re_l * mu_l / d_i * 60.**2 # Pa s/m * 60^2s/h = kg/m^2/h\n",
    "m_dot_l = g_l * np.pi/4*(d_i**2 - 2500.*0.0254**2) # kg/m^2/h * m^2 = kg/h\n",
    "u_s_l = g_l/rho_l # kg/m^2/h *m^3/kg = m/h \n",
    "\n",
    "output = [\n",
    "    'Kühlmittel: Wasser bei Sättigung bei 230°C ' +\n",
    "    '(' + str(230+273.15) + 'K, ' +\n",
    "    '28bar) (VDI-Wärmeatlas)',\n",
    "    'rho_l = ' + '{:g}'.format(rho_l) + ' kg/m^3',\n",
    "    'cp_l = ' + '{:g}'.format(cp_l) + ' kJ/kg/K',\n",
    "    'eta_l = ' + '{:g}'.format(eta_l) + ' Pa s',\n",
    "    'Pr_l = ' + '{:g}'.format(pr_l) + ' ',\n",
    "    'Voll-ausgebildete turbulente Strömung:',\n",
    "    'Re_l = ' + '{:g}'.format(re_l) + ' ',\n",
    "    '==>> G_l = ' + '{:g}'.format(g_l) + ' kg/m^2/h',\n",
    "    '==>> m_dot_l = ' + '{:g}'.format(m_dot_l) + ' kg/h',\n",
    "    '==>> u_s_l = ' + '{:g}'.format(u_s_l) + ' m/h',\n",
    "    'Nusselt-Zahl bei voll-ausgebildeter turbulenter' +\n",
    "    'Strömung (Gl. 26 Kap. G1 VDI-Wärmeatlas)',\n",
    "    'xi_l = ' + '{:g}'.format(xi_l) + ' ',\n",
    "    'Nu_l = ' + '{:g}'.format(nu_l) + ' ',\n",
    "    'Bezugslänge: Innendurchmesser des Rohrbündels ' +\n",
    "    'mit 2500 Rohren, je 2,54cm',\n",
    "    'd_i = ' + '{:g}'.format(d_i) + ' m',\n",
    "    'Wärmeübergangskoeffizient im Mantel',\n",
    "    'alpha_o = '  + '{:g}'.format(alpha_o) + \n",
    "    ' kcal/h/m^2/°C',\n",
    "]\n",
    "print('\\n'.join(output))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prozessstrom Kennzahlen\n",
      "Pr = 3.14859 \n",
      "Re = 128.313 \n",
      "==>> G = 4684 kg/m^2/h\n",
      "==>> m_dot = 12780.5 kg/h\n",
      "==>> u_s = 3622.58 m/h\n",
      "Nusselt-Zahl mit ruhenden Feststoffpartikeln\n",
      "(Schüttschicht), nach Levas Korrelation in \n",
      "Behr Gmehling Techn. Chemie\n",
      "Nu = 60.8 \n",
      "Bezugslänge: Innendurchmesser des Rohrbündels \n",
      "d = 0.0254 m\n",
      "Wärmeübergangskoeffizient im Rohr\n",
      "alpha_i = 88.4539 kcal/h/m^2/°C\n",
      "Mittlerer Wärmeübergangskoeffizient\n",
      "U = 82.7 kcal/h/m^2/°C\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x192c2bfb390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy import integrate\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "l_r = 3 # m\n",
    "d = 2.54 *1/100. # m\n",
    "n = 2500 # Rohre\n",
    "t=t0\n",
    "dp = 3/1000. # m\n",
    "rho_b = 1300# Bulk density = rhoc*(1-phi) # kgKat/m^3\n",
    "p = 1 # atm\n",
    "n_p = 1650 # t/a\n",
    "g = 1650*1000./365./24./2500./(3.14/4*0.025**2)\n",
    "g = 4684 # kg / m^2/h\n",
    "rho_g = 1.293 # kg/m^3\n",
    "m_dot = g * np.pi/4*d_i**2 # kg/m^2/h * m^2 = kg/h\n",
    "u_s = g/rho_g # m^3/m^2/h\n",
    "delta_h_r = -307000. # kcal/kmol \n",
    "cp = 0.237 # kcal/(kg °C) \n",
    "pb0 = y_i[1] * 1 # atm\n",
    "\n",
    "re = dp*g/mu * 1/60.**2 # dp*g/mu [=] \n",
    "# m * kg/m^2/h /kg *m*s = [dimlos]\n",
    "pr = mu/(lambda_g/(cp_g*4.184*1000.))\n",
    "# Pr[=] kg/m/s /J *s*m*K * kcal/kg/K * 4.184kJ/kcal *\n",
    "# 1000J/kJ [=] [dimlos]\n",
    "\n",
    "# Leva's Korrelation\n",
    "nu = 3.50 * (re)**0.7*np.exp(-4.6*dp/d)\n",
    "alpha_i = nu * lambda_g / d /4.184/1000*60**2# W/m^2/K\n",
    "# * 1cal/4.184J * 1kcal/1000cal * 60^2s/h = kcal/h/m^2/K\n",
    "u = 1/(1/alpha_i + w_d/lambda_m  + 1/alpha_o)\n",
    "\n",
    "def df_dy(y, z0):\n",
    "    p = y[0]\n",
    "    t = y[1]\n",
    "    k_t = np.exp(19.837-13636/t) \n",
    "    # k_t[=] kmol/kgKat/h * atm^-2\n",
    "    r_a = k_t * pb0 * p # kmol/kgKat/h\n",
    "    dp_dz = -mm_g*1*rho_b/rho_g*r_a/u_s\n",
    "    dt_dz = -delta_h_r/(\n",
    "        rho_g*cp\n",
    "    )* rho_b * r_a/(u_s) - 4/d * u/(\n",
    "        rho_g*cp)/(u_s)*(t-t0)\n",
    "    return np.array([dp_dz, dt_dz])\n",
    "\n",
    "z = np.linspace(0, 3.0, 100)\n",
    "\n",
    "pb0 = y_i[1] * 1 # atm\n",
    "mm_g = np.array([28, 32, 40, 78.11]) # g/mol\n",
    "mm_g = sum(y_i * mm_g).item()\n",
    "p0_t0 = np.array([y_i[-1]*1,t0])\n",
    "y, info = integrate.odeint(\n",
    "    df_dy, p0_t0, z, full_output=True\n",
    ")\n",
    "\n",
    "output = [\n",
    "    'Prozessstrom Kennzahlen',\n",
    "    'Pr = ' + '{:g}'.format(pr) + ' ',\n",
    "    'Re = ' + '{:g}'.format(re) + ' ',\n",
    "    '==>> G = ' + '{:g}'.format(g) + ' kg/m^2/h',\n",
    "    '==>> m_dot = ' + '{:g}'.format(m_dot) + ' kg/h',\n",
    "    '==>> u_s = ' + '{:g}'.format(u_s) + ' m/h',\n",
    "    'Nusselt-Zahl mit ruhenden Feststoffpartikeln\\n' +\n",
    "    '(Schüttschicht), nach Levas Korrelation in \\n' + \n",
    "    'Behr Gmehling Techn. Chemie',\n",
    "    'Nu = ' + '{:g}'.format(nu) + ' ',\n",
    "    'Bezugslänge: Innendurchmesser des Rohrbündels ',\n",
    "    'd = ' + '{:g}'.format(d) + ' m',\n",
    "    'Wärmeübergangskoeffizient im Rohr',\n",
    "    'alpha_i = '  + '{:g}'.format(alpha_i) + \n",
    "    ' kcal/h/m^2/°C',\n",
    "    'Mittlerer Wärmeübergangskoeffizient',\n",
    "    'U = '  + '{:g}'.format(u) + \n",
    "    ' kcal/h/m^2/°C',\n",
    "]\n",
    "print('\\n'.join(output))\n",
    "    \n",
    "    \n",
    "fig = plt.figure(1)\n",
    "fig.set_size_inches(20*12/30.48, 30*12/30.48)\n",
    "ax1 = plt.subplot(211)\n",
    "plt.setp(ax1.get_xticklabels(), visible=False)\n",
    "ax2 = plt.subplot(212,  sharex=ax1)\n",
    "ax1.set_ylim([0, 0.02])\n",
    "ax2.set_ylim([625, 740])\n",
    "ax1.set_xlim([0,1.25])\n",
    "ax1.set_ylabel('$p_0 / atm$')\n",
    "ax2.set_ylabel('T / K')\n",
    "ax2.set_xlabel('z / m')\n",
    "\n",
    "p_werte = [0.011, 0.012, 0.013, 0.014, \n",
    "           0.015, 0.016, 0.017, 0.018,\n",
    "          0.0181, 0.0182, 0.019]\n",
    "\n",
    "soln = np.zeros([len(p_werte), len(z), 2])\n",
    "\n",
    "for i, p0 in enumerate(p_werte):    \n",
    "    y_i = np.array([78,21,1,p0*100])/sum(\n",
    "        np.array([78,21,1,p0*100], dtype=float))\n",
    "    pb0 = y_i[1] * 1 # atm\n",
    "    p0_t0 = np.array([y_i[-1],t0])\n",
    "    y, info = integrate.odeint(\n",
    "        df_dy, p0_t0, z, full_output=True\n",
    "    )\n",
    "    soln[i, :, :] = y\n",
    "    \n",
    "    plt.figure(1)    \n",
    "    ax1.plot(z, y[:,0], label=str(p0));\n",
    "    ax2.plot(z, y[:, 1], label=str(p0));\n",
    "    \n",
    "    index_max = np.argmax(y[:,1])\n",
    "    x_max = z[index_max]\n",
    "    y_max = y[index_max,1]\n",
    "    \n",
    "    ax2_lim = ax2.get_ylim()\n",
    "    if y_max < max(ax2_lim):\n",
    "        ax2.annotate('$p_0=' + str(p0) + '$', \n",
    "                     xy=(x_max, y_max))\n",
    "\n",
    "ax1.legend()\n",
    "ax2.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 11.5.c-1 Froment Bischoff\n",
    "(7.2.1 Behr Gmehling) Wärmeexplosion / Run-away\n",
    "\n",
    "Man nehmbeziehe sich auf den Gleichungen aus 11.5.b.\n",
    "\n",
    "$r_A=k p_B^{\\circ}p$\n",
    "\n",
    "$ln(k) =19.837-\\frac{13.636}{T}$\n",
    "\n",
    "Anmerkung: Nach Notation dieses Buches(S. XVII, oder S. 14) bestehen die folgenden Einheiten: $k_A[=] \\frac{kmol}{kgKat\\cdot h}\\cdot atm^{-2}$,\n",
    "$r_A[=] \\frac{kmol}{kgKat\\cdot h} $\n",
    "\n",
    "Kontinuität, Energie:\n",
    "\n",
    "$u_s\\frac{dp}{dz}+\n",
    "\\frac{M_m p_t \\rho_B}{\\rho_g}k p_B^{\\circ}p=0$\n",
    "\n",
    "$u_s \\rho_g c_p \\frac{dT}{dz}-\n",
    "(-\\Delta H)\\rho_B k p_B^{\\circ}p + \n",
    "\\frac{4 U}{d_t}(T-T_r)=0$\n",
    "\n",
    "Anmerkung: $T$, Prozessstromtemperatur; $Tr$, Umgebungstemperatur (Temperatur der Wand)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Phasenebene wird durch Division der Energiebilanz durch die Kontinuität-Gl. erhalten:\n",
    "\n",
    "$\\begin{array}{lllll}\n",
    "\\frac{dT}{dp} &= \\frac{(-\\Delta_H)}{M_m p_t C_p}& - \\frac{4 U}{C_p d_t} &\\cdot\\frac{1}{p_B^{\\circ}M_m p_t \\rho_B}\\cdot &\\frac{(T-Tr)}{p \\cdot exp\\left(-\\frac{R}{R T}+b\\right)\\frac{kmol}{kgKat \\cdot h}\\cdot atm^{-2}}\\\\\n",
    "\\frac{dT}{dp} &= -\\frac{B\\cdot}{A} & + C\\cdot \\rho_g&\\cdot\\frac{1}{A\\cdot \\rho_g} \\cdot& \\frac{(T-Tr)}{p \\cdot exp\\left(-\\frac{R}{R T}+b\\right)\\frac{kmol}{kgKat \\cdot h}\\cdot atm^{-2}}\n",
    "\\end{array}$\n",
    "\n",
    "$\\Rightarrow A = \\frac{M_m p_t \\rho_B}{\\rho_g}p_B^{\\circ} \\\\\n",
    "\\quad B = \\frac{(-\\Delta H)\\rho_B}{\\rho_g C_p}p_B^{\\circ}\\\\\n",
    "\\quad C=\\frac{4 U}{\\rho_g C_p d_t}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Maximaler Verlauf der Phasebebene liegt bei $\\frac{dT}{dp}=0$: \"Maximakurve\"\n",
    "\n",
    "$\\Rightarrow p_m = \\frac{(T-Tr)}{\\frac{B\\cdot}{C} \\cdot exp\\left(-\\frac{R}{R T}+b\\right)\\frac{kmol}{kgKat \\cdot h}\\cdot atm^{-2}}$\n",
    "\n",
    "Die Kurve selbst besitzt den Maximalwert:\n",
    "\n",
    "$T_M=\\frac{1}{2}\\left[\\frac{E}{R}-\\sqrt{\\frac{E}{R}\\left(\\frac{E}{R}-4T_r\\right)}\\right]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T0 = 625.15 K\n",
      "A = 6190.4 kgKat/kmol atm^2\n",
      "B = 2.68398e+08 kgKat/kmol atm K\n",
      "C = 42499.6 1/h\n",
      "A/B = 2.30642e-05 atm/K\n",
      "B/A = 43357.2 K/atm\n",
      "C/A = 6.86541 kmol/kgKat/h atm^-2\n",
      "B/C = 6315.32 kgKat/kmol atm K h\n",
      "Q = 4.16047 [dimensionslos]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x192c297e438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t0 = 352 + 273.15 # K\n",
    "t=t0\n",
    "rho_b = 1300# Bulk density = rhoc*(1-phi) # kgKat/m^3\n",
    "p_t = 1 # atm\n",
    "rho_g = 1.293 # kg/m^3\n",
    "delta_h_r = -307000. # kcal/kmol \n",
    "cp = 0.237 # kcal/(kg °C) \n",
    "y_i = np.array([78,21,1.,p0*100.])/sum(\n",
    "    np.array([78,21,1,p0*100.], dtype=float))\n",
    "pb0 = y_i[1] * 1 # atm\n",
    "mm_g = sum(\n",
    "    y_i * np.array([28, 32, 40, 78.11])\n",
    ").item() # g/mol\n",
    "\n",
    "d_t = 2.54 *1/100. # m\n",
    "u = 82.7 # kcal/m^2/h\n",
    "\n",
    "a = mm_g*1*rho_b/rho_g*pb0 # kgKat/kmol atm^2\n",
    "b = -delta_h_r*rho_b/(rho_g * cp)*pb0 # kgKat/kmol atm K\n",
    "c = 4*u/(rho_g * cp * d_t) # 1/h\n",
    "e_d_r = 13636. # 1/K\n",
    "b_kin = 19.837 # dimlos\n",
    "\n",
    "tm = np.linspace(t0, np.max(soln[:,:,1]), 100)\n",
    "pm = (tm - t0)/(b/c * np.exp(-e_d_r/tm+b_kin))\n",
    "\n",
    "tmax = 1/2*(e_d_r-np.sqrt(e_d_r*(e_d_r-4*t0)))\n",
    "pmax = (tmax - t0)/(b/c * np.exp(-e_d_r/tmax+b_kin))\n",
    "q = 1/np.sqrt(a/c * np.exp(-e_d_r/tmax+b_kin))\n",
    "\n",
    "output = [\n",
    "    'T0 = ' + '{:g}'.format(t0) + ' K', \n",
    "    'A = ' + '{:g}'.format(a) + ' kgKat/kmol atm^2',\n",
    "    'B = ' + '{:g}'.format(b) + ' kgKat/kmol atm K',\n",
    "    'C = ' + '{:g}'.format(c) + ' 1/h',\n",
    "    'A/B = ' + '{:g}'.format(a/b) + ' atm/K',\n",
    "    'B/A = ' + '{:g}'.format(b/a) + ' K/atm',\n",
    "    'C/A = ' + '{:g}'.format(c/a) + \n",
    "    ' kmol/kgKat/h atm^-2',\n",
    "    'B/C = ' + '{:g}'.format(b/c) + \n",
    "    ' kgKat/kmol atm K h',\n",
    "    'Q = ' + '{:g}'.format(q) + \n",
    "    ' [dimensionslos]',\n",
    "]\n",
    "print('\\n'.join(output))\n",
    "\n",
    "fig2 = plt.figure(2)\n",
    "fig2.set_size_inches(30*12/30.48, 20*12/30.48)\n",
    "ax3 = plt.subplot(111)\n",
    "ax3.set_xlim([625, 700])\n",
    "ax3.set_ylim([0, 0.03])\n",
    "ax3.set_ylabel('$p_0 / atm$')\n",
    "ax3.set_xlabel('T / K')\n",
    "\n",
    "maxima_p = np.zeros(len(p_werte))\n",
    "maxima_t = np.zeros(len(p_werte))\n",
    "\n",
    "for i, p0 in enumerate(p_werte):\n",
    "    y_i = np.array([78,21,1,p0*100])/sum(\n",
    "        np.array([78,21,1,p0*100], dtype=float))\n",
    "    pb0 = y_i[1] * 1 # atm\n",
    "    p0 = y_i[-1] * 1 # atm\n",
    "    \n",
    "    index_max = np.argmax(soln[i,:,1])\n",
    "    maxima_p[i] = soln[i,index_max,0]\n",
    "    maxima_t[i] = soln[i,index_max,1]\n",
    "    p = soln[i,:,0]\n",
    "    t = soln[i,:,1]\n",
    "    ax3.plot(t, p)\n",
    "    if maxima_t[i] < max(ax3.get_xlim()):\n",
    "        ax3.annotate('$p_0=' + \n",
    "                     '{:0.3g}'.format(p_werte[i]) + \n",
    "                     '$', \n",
    "                     xy=(soln[i,index_max,1],\n",
    "                     soln[i,index_max,0]))\n",
    "    # Adiabate Verläufe\n",
    "    t = np.linspace(t0, tmax, 2)\n",
    "    if i<1:\n",
    "        label = 'Adiabate Steigung am Einlass'\n",
    "    else:\n",
    "        label = ''\n",
    "    ax3.plot(t, -a/b*(t-t0)+p0,\n",
    "             ls='dotted', color='gray',\n",
    "             label=label)\n",
    "        \n",
    "ax3.plot(maxima_t, maxima_p, 'o', color='black')\n",
    "ax3.plot(tm, pm, '--', color='black',\n",
    "        label=r'$p_m = \\frac{(T-Tr)}{\\frac{B\\cdot}{C}'+\n",
    "         r' \\cdot exp\\left(-\\frac{R}{R T}+b\\right)'+\n",
    "         r'\\frac{kmol}{kgKat \\cdot h}\\cdot atm^{-2}}$')\n",
    "t = np.linspace(t0, tmax, 2)\n",
    "p_0_l =  -a/b*(t-t0) + a/b*(tmax-t0)*(1+q**2)\n",
    "ax3.plot(t, p_0_l, label='$p_0^l$', \n",
    "         linestyle=(0, (5, 1)),\n",
    "        linewidth=2)\n",
    "ax3.text(t[0], p_0_l[0], '$p_0^l$=' + \n",
    "         '{:g}'.format(p_0_l[0]))\n",
    "ax3.annotate(\n",
    "    r'$T_M=\\frac{1}{2}\\left[\\frac{E}{R}-\\sqrt{'+\n",
    "    r'\\frac{E}{R}\\left(\\frac{E}{R}-4 T_r\\right)'+\n",
    "    r'}\\right]$= '+'{:g}'.format(tmax)+' K',\n",
    "    xy=[tmax, pmax], \n",
    "    xytext=[+50,+70],\n",
    "    textcoords='offset points',\n",
    "    arrowprops=dict(\n",
    "        arrowstyle='->',\n",
    "        connectionstyle='angle,angleA=0,angleB=90,rad=10'\n",
    "    ),\n",
    "    size=15\n",
    ")\n",
    "font = dict(\n",
    "    [['family','arial'],['size',20]]\n",
    ")\n",
    "ax3.legend(prop=font);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x23fdb256518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(311)\n",
    "ax1.plot(z,soln[8,:,1])\n",
    "ax2 = fig.add_subplot(312)\n",
    "ax2.plot(z,np.gradient(soln[8,:,1]))\n",
    "ax2.axhline(0, linestyle='--')\n",
    "ax3 = fig.add_subplot(313)\n",
    "ax3.plot(z,np.gradient(np.gradient(soln[8,:,1])))\n",
    "ax3.axhline(0, linestyle='--');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Teil 1** Erforderliche Eintrittspartialdruckwerte für gegebene Eintrittstemperaturen und Rohrradien."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T0 = 625 K\n",
      "A = 6165.04 kgKat/kmol atm^2\n",
      "B = 2.57006e+08 kgKat/kmol atm K\n",
      "C = 40965.9 1/h\n",
      "A/B = 2.39879e-05 atm/K\n",
      "B/A = 41687.6 K/atm\n",
      "C/A = 6.64488 kmol/kgKat/h atm^-2\n",
      "B/C = 6273.64 kgKat/kmol atm K h\n",
      "Q = 4.10386 [dimensionslos]\n",
      "kritische Temperatur: 656.618 K\n",
      "Partialdruck bei kritischem Pfad: 0.0127737 atm\n",
      "Delta T_max = 31.6183 K\n",
      "Delta T_zulässig = 564.125 K\n",
      "$p_{0,NG}=0.0135322 atm$\n",
      "$p_{0,M}=0.0166448 atm$\n",
      "$p_{0,OG}=0.0197574 atm$\n",
      "$p_{0,OG-10\\%}=0.0177817 atm$\n",
      "$p_{0,Rückintegration}=0.016297 atm$\n",
      "\n",
      "Tabelle 1\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\users\\public\\apps\\anaconda3\\lib\\site-packages\\ipykernel_launcher.py:38: RuntimeWarning: overflow encountered in exp\n",
      "c:\\users\\public\\apps\\anaconda3\\lib\\site-packages\\scipy\\integrate\\odepack.py:218: ODEintWarning: Excess accuracy requested (tolerances too small). Run with full_output = 1 to get quantitative information.\n",
      "  warnings.warn(warning_msg, ODEintWarning)\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\begin{array}{lllll}\\hline & & \\Delta T_{ad}  & p_0(atm)& p_0(bar)\\\\\\hline\\\\\\text{Unterer Grenzwert} & \\Delta T(1+Q^2) &=564.125K& 0.0135322& 0.0137115\\\\\\text{Oberer Grenzwert} & \\Delta T(1+Q)^2 &=823.639K& 0.0197574& 0.0200192\\\\\\text{Mittelwert} & \\Delta T(1+Q+Q^2) &=693.882K& 0.0166448& 0.0168654\\\\\\end{array}$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x192c2bc00f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.display import Latex\n",
    "\n",
    "t0 = 625 # K\n",
    "rt = d/2. # m\n",
    "rt = 0.0125 # m\n",
    "\n",
    "y_i = np.array([78,21,1,1])/sum(\n",
    "        np.array([78,21,1,1], dtype=float))\n",
    "pb0 = y_i[1] * 1 # atm\n",
    "p0 = y_i[-1] * 1 # atm\n",
    "pb0 = 0.208 # atm\n",
    "mm_g = np.array([28, 32, 40, 78.11]) # g/mol\n",
    "mm_g = sum(y_i * mm_g).item()\n",
    "mm_g = 29.48 # kg/kgmol\n",
    "rho_g = 1.293 # kg/m^3\n",
    "cp = 0.323/1.293 # kcal/kg\n",
    "\n",
    "a = mm_g*1*rho_b/rho_g*pb0 # kgKat/kmol atm^2\n",
    "b = -delta_h_r*rho_b/(rho_g * cp)*pb0 # kgKat/kmol atm K\n",
    "c = 4*u/(rho_g * cp * 2*rt) # 1/h\n",
    "#a=6150\n",
    "#b=257e6\n",
    "#c=41000\n",
    "\n",
    "e_d_r = 13636. # 1/K\n",
    "b_kin = 19.837 # dimlos\n",
    "\n",
    "tm = np.linspace(t0, np.max(soln[:,:,1]), 100)\n",
    "pm = (tm - t0)/(b/c * np.exp(-e_d_r/tm+b_kin))\n",
    "\n",
    "tmax = 1/2*(e_d_r-np.sqrt(e_d_r*(e_d_r-4*t0)))\n",
    "pmax = (tmax - t0)/(b/c * np.exp(-e_d_r/tmax+b_kin))\n",
    "q = 1/np.sqrt(a/c * np.exp(-e_d_r/tmax+b_kin))\n",
    "#q=2.9203\n",
    "\n",
    "delta_t_max = tmax - t0\n",
    "delta_t_zul_ng = delta_t_max * (1+q**2)\n",
    "p0_zul_ng = delta_t_zul_ng * a/b\n",
    "delta_t_zul_og = delta_t_max * (1+q)**2\n",
    "p0_zul_og = delta_t_zul_og * a/b\n",
    "delta_t_zul_m = delta_t_max * (1+q+q**2)\n",
    "p0_zul_m = delta_t_zul_m * a/b\n",
    "p0_zul_og_minus10pzt = 0.9*p0_zul_og\n",
    "\n",
    "# Numerische Rückintegration\n",
    "def dy_dz(y, zeit_t0):\n",
    "    p = y[0]\n",
    "    t = y[1]\n",
    "    k = np.exp(-e_d_r/t+b_kin)\n",
    "    dp_dz = -a/u_s * k * p\n",
    "    dt_dz = b/u_s * k * p -c/u_s * (t-t0)\n",
    "    return np.array([dp_dz, dt_dz])\n",
    "\n",
    "z = np.linspace(0,-1, 200)\n",
    "p0_t0 = np.array([pmax,tmax])\n",
    "y, info = integrate.odeint(\n",
    "    df_dy, p0_t0, z, full_output=True\n",
    ")\n",
    "# Alles, bishin zu Singularitäten oder T=0 nehmen\n",
    "min_index = np.where(np.isnan(y[:,1]))[0][0]\n",
    "# z=0 bei T=T_0 bestimmen\n",
    "z0_rueckint = interp1d(\n",
    "    y[:min_index,1],z[:min_index])(t0).item()\n",
    "p0_rueckint = interp1d(\n",
    "    z[:min_index],y[:min_index,0])(z0_rueckint).item()\n",
    "# Vorwärtsintegration für grafische Darstellung\n",
    "# (weil man es kann)\n",
    "z = np.linspace(0,3, 100)\n",
    "p0_werte = [p0_zul_ng, \n",
    "            p0_zul_m, \n",
    "            p0_zul_og, \n",
    "            p0_zul_og_minus10pzt,\n",
    "            p0_rueckint]\n",
    "labels = ['$p_{0,NG}='+'{:g}'.format(p0_zul_ng)+' atm'+'$',\n",
    "          '$p_{0,M}='+'{:g}'.format(p0_zul_m)+' atm'+'$',\n",
    "          '$p_{0,OG}='+'{:g}'.format(p0_zul_og)+' atm'+'$',\n",
    "          '$p_{0,OG-10\\%}='+'{:g}'.format(\n",
    "              p0_zul_og_minus10pzt)+' atm'+'$',\n",
    "          '$p_{0,Rückintegration}='+\n",
    "          '{:g}'.format(p0_rueckint)+' atm'+'$']\n",
    "soln = np.empty([len(p0_werte), z.size, 2])\n",
    "\n",
    "for i, p0_wert in enumerate(p0_werte):\n",
    "    p0_t0 = np.array([p0_wert,t0])\n",
    "    y, info = integrate.odeint(\n",
    "        df_dy, p0_t0, z, full_output=True\n",
    "    )\n",
    "    soln[i, :, 0] = y[:,0]\n",
    "    soln[i, :, 1] = y[:,1]    \n",
    "\n",
    "fig = plt.figure()\n",
    "fig.set_size_inches(20*12/30.48, 30*12/30.48)\n",
    "ax1 = fig.add_subplot(311)\n",
    "ax2 = fig.add_subplot(312, sharex=ax1)\n",
    "ax3 = fig.add_subplot(313)\n",
    "\n",
    "plt.setp(ax1.get_xticklabels(), visible=False)\n",
    "ax1.set_ylim([0, 0.02])\n",
    "ax2.set_ylim([625, 740])\n",
    "ax1.set_xlim([0,1.25])\n",
    "ax3.set_xlim([t0,700])\n",
    "ax3.set_ylim([0,0.03])\n",
    "ax1.set_ylabel('$p / atm$')\n",
    "ax2.set_ylabel('T / K')\n",
    "ax2.set_xlabel('z / m')\n",
    "ax3.set_xlabel('T / K')\n",
    "ax3.set_ylabel('$p / atm$')\n",
    "\n",
    "for i, p0_wert in enumerate(p0_werte):\n",
    "    ax1.plot(z,soln[i,:,0], label=labels[i])\n",
    "    ax2.plot(z,soln[i,:,1], label=labels[i])\n",
    "    ax3.plot(soln[i,:,1],soln[i,:,0], label=labels[i])\n",
    "ax3.plot(tm, pm, '--', color='black',\n",
    "        label=r'$p_m = \\frac{(T-Tr)}{\\frac{B\\cdot}{C}'+\n",
    "         r' \\cdot exp\\left(-\\frac{R}{R T}+b\\right)'+\n",
    "         r'\\frac{kmol}{kgKat \\cdot h}\\cdot atm^{-2}}$')\n",
    "ax3.annotate(\n",
    "    r'$T_M=\\frac{1}{2}\\left[\\frac{E}{R}-\\sqrt{'+\n",
    "    r'\\frac{E}{R}\\left(\\frac{E}{R}-4 T_r\\right)'+\n",
    "    r'}\\right]$= '+'{:g}'.format(tmax)+' K',\n",
    "    xy=[tmax, pmax], \n",
    "    xytext=[-130,+70],\n",
    "    textcoords='offset points',\n",
    "    arrowprops=dict(\n",
    "        arrowstyle='->',\n",
    "        connectionstyle='angle,angleA=0,angleB=90,rad=10'\n",
    "    ),\n",
    "    size=10\n",
    ")\n",
    "font = dict(\n",
    "    [['family','arial'],['size',10]]\n",
    ")\n",
    "ax1.legend(prop=font)\n",
    "ax2.legend(prop=font)\n",
    "ax3.legend(prop=font)\n",
    "\n",
    "output = [\n",
    "    'T0 = ' + '{:g}'.format(t0) + ' K', \n",
    "    'A = ' + '{:g}'.format(a) + ' kgKat/kmol atm^2',\n",
    "    'B = ' + '{:g}'.format(b) + ' kgKat/kmol atm K',\n",
    "    'C = ' + '{:g}'.format(c) + ' 1/h',\n",
    "    'A/B = ' + '{:g}'.format(a/b) + ' atm/K',\n",
    "    'B/A = ' + '{:g}'.format(b/a) + ' K/atm',\n",
    "    'C/A = ' + '{:g}'.format(c/a) + \n",
    "    ' kmol/kgKat/h atm^-2',\n",
    "    'B/C = ' + '{:g}'.format(b/c) + ' kgKat/kmol atm K h',\n",
    "    'Q = ' + '{:g}'.format(q) + ' [dimensionslos]',\n",
    "    'kritische Temperatur: ' + '{:g}'.format(tmax) + ' K',\n",
    "    'Partialdruck bei kritischem Pfad: ' + \n",
    "    '{:g}'.format(pmax) + ' atm',\n",
    "    'Delta T_max = ' + '{:g}'.format(\n",
    "        delta_t_max) + ' K',     \n",
    "    'Delta T_zulässig = ' + '{:g}'.format(\n",
    "        delta_t_zul_ng) + ' K',    \n",
    "    *labels,\n",
    "    ''\n",
    "]\n",
    "print('\\n'.join(output))\n",
    "\n",
    "print('Tabelle 1')\n",
    "\n",
    "Latex(\n",
    "    '$' +\n",
    "    r'\\begin{array}{lllll}'+\n",
    "    r'\\hline'+\n",
    "    r' & & \\Delta T_{ad}  & p_0(atm)& p_0(bar)\\\\'+\n",
    "    r'\\hline\\\\'+\n",
    "    r'\\text{Unterer Grenzwert} & \\Delta T(1+Q^2) &=' + \n",
    "    '{:g}'.format(delta_t_zul_ng) + 'K' +\n",
    "    r'& ' + '{:g}'.format(p0_zul_ng) + \n",
    "    r'& ' + '{:g}'.format(p0_zul_ng*1.01325) + r'\\\\'+\n",
    "    r'\\text{Oberer Grenzwert} & \\Delta T(1+Q)^2 &=' + \n",
    "    '{:g}'.format(delta_t_zul_og) + 'K' +\n",
    "    r'& ' + '{:g}'.format(p0_zul_og) + \n",
    "    r'& ' + '{:g}'.format(p0_zul_og*1.01325) + r'\\\\'+\n",
    "    r'\\text{Mittelwert} & \\Delta T(1+Q+Q^2) &=' + \n",
    "    '{:g}'.format(delta_t_zul_m) + 'K' +\n",
    "    r'& ' + '{:g}'.format(p0_zul_m) + \n",
    "    r'& ' + '{:g}'.format(p0_zul_m*1.01325) + r'\\\\'+\n",
    "    r'\\end{array}'+\n",
    "    '$'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Teil 2** Kritischer Radius bei gegebenem Druck $p_0$=0,0125atm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2. Kritischer Radius bei gegebenem Druck p0, Temperatur Tr\n",
      "kritische Temperatur: 656.618 K\n",
      "q_krit = 3.46621 [dimensionslos]\n",
      "C_krit = 29224.4 1/h\n",
      "r_krit = 0.0175221 m\n"
     ]
    }
   ],
   "source": [
    "p0 = 0.0125 # atm\n",
    "t0 = 625 # K\n",
    "# Q, aus dem Mittelwert ermittelt (Gl. 11.5.c-6)\n",
    "q_k = (-1+np.sqrt(1-4*(1-p0*b/a*1/(tmax-t0))))/2.\n",
    "c_k = q_k**2 * a * np.exp(-e_d_r/tmax+b_kin)\n",
    "r_k = 4*u/(rho_g * cp) * 1/c_k * 1/2.\n",
    "output = [\n",
    "    '2. Kritischer Radius bei gegebenem Druck p0, Temperatur Tr',\n",
    "    'kritische Temperatur: ' + \n",
    "    '{:g}'.format(tmax) + ' K',\n",
    "    'q_krit = ' + '{:g}'.format(q_k) + ' [dimensionslos]',\n",
    "    'C_krit = ' + '{:g}'.format(c_k) + ' 1/h',\n",
    "    'r_krit = ' + '{:g}'.format(r_k) + ' m',\n",
    "]\n",
    "print('\\n'.join(output))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Teil 3** Unterkritische Bedingungen, Druck p0=0,0075atm, Radius Rt=0,0125m, Heißpunkt-Temperatur (hotspot) TM=675K. Wandtemperatur? (Tr=T0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3. Unterkritische Bedingungen. p0=0,0074atm, Radius 0,0125m. Wandtemperatur, damit Heißpunkt sich bei 675K befindet?\n",
      "kritische Temperatur: 675 K\n",
      "Wandtemperatur: 641.587 K\n",
      "Q = 3.17794 [dimensionslos]\n",
      "Bei dieser Temperatur obere und niedrige Grenzwerte für p0:\n",
      "$p_{0,NG}=0.00843069 atm$\n",
      "$p_{0,M}=0.0108445 atm$\n",
      "$p_{0,OG}=0.0132584 atm$\n",
      "$p_{0,OG-10\\%}=0.0119326 atm$\n",
      "$p_{0,Rückintegration}=0.0106507 atm$\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\users\\public\\apps\\anaconda3\\lib\\site-packages\\ipykernel_launcher.py:38: RuntimeWarning: overflow encountered in exp\n",
      "c:\\users\\public\\apps\\anaconda3\\lib\\site-packages\\scipy\\integrate\\odepack.py:218: ODEintWarning: Illegal input detected (internal error). Run with full_output = 1 to get quantitative information.\n",
      "  warnings.warn(warning_msg, ODEintWarning)\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\begin{array}{lllll}\\hline & & \\Delta T_{ad}  & p_0(atm)& p_0(bar)\\\\\\hline\\\\\\text{Unterer Grenzwert} & \\Delta T(1+Q^2) &=370.866K& 0.00843069& 0.00854239\\\\\\text{Oberer Grenzwert} & \\Delta T(1+Q)^2 &=583.238K& 0.0132584& 0.0134341\\\\\\text{Mittelwert} & \\Delta T(1+Q+Q^2) &=477.052K& 0.0108445& 0.0109882\\\\\\end{array}$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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

lvkg.py

rvm_001.jpg

van_den_bussche_froment.ipynb

vdb_f_chp_01.ipynb

vdb_f_r_flb_01.png

vdb_f_r_flb_01.tex

wgs_001.jpg

wgs_r.ipynb